Factoring The difference of two squares

Solve Quadratic Equations using the Distributive Property and Factoring by the Difference of Two Squares

Grade 8 identifying the techniques to be used given a polynomial with the choices factoring polynomials, difference of two squares, sum and difference of two cubes, factoring perfect square trinomial, factoring quadratic trinomials and factoring trinomials

Factorising using the difference of two squares

To the Lakota, and other indigenous people on North America's Great Plains, the bison was an essential part of their culture ( expressed in the quote on the previous page). The bison provided meat for nutrition, a hide for clothing and shelter, bones for tools, and fat for soap. The bison was also central to their religious beliefs. So, when European settlers hunted the bison nearly to extinction, Lakota culture suffered. Culture is central to a society and the identity of its people, as well as its continued existence. Therefore, geographers study culture as a way to understand similarities and differences among societies across the world, and in some cases, to help preserve these societies. Analyzing Culture All of a group's learned behaviors, actions, beliefs, and objects are a part of culture. It is a visible force seen in a group's actions, possessions, and influence on the landscape. For example, in a large city you can see people working in offices, factories, and stores, and living in high-rise apartments or suburban homes. You might observe them attending movies, concerts, or sporting events. Culture is also an invisible force guiding people through shared belief systems, customs, and traditions. Culture is learned, in that it develops through experiences, and not merely transmitted through genetics. For example, many people in the United States have developed a strong sense of competitiveness in school and business, and believe that hard work is a key to success. These types of elements, visible and invisible, are cultural traits. A series of interrelated traits make up a cultural complex, such as the process of steps and acceptable behaviors related to greeting a person in different cultures. A single cultural artifact, such as an automobile, may represent many different values, beliefs, behaviors and traditions and be representative of a cultural complex. Since culture is learned there are many ways that one generation passes its culture to the next. Children and adults learn traits three ways: • imitation, as when learning a language by repeating sounds or behaviors from a person or television • informal instruction, as when a parent reminds a child to say "please" • formal instruction, as when students learn history in school 132 HUMAN GEOGRAPHY: AP" EDITION CULTURAL COMPLEX OF THE AUTOMOBILE The automobile provides much more than just transportation, as it reflects many values that are central to American culture. Origins of Culture The area in which a unique culture or a specific trait develops is a culture hearth. Classical Greece was a culture hearth for democracy more than 2,000 years ago. New York City was a culture hearth for rap music in the 1970s. Geographers study how cultures develop in hearths and diffuse-or spread-to other places. Geographers also study taboos, behaviors heavily discouraged by a culture. For example, many cultures have taboos against eating certain foods, such as pork or insects. What is considered taboo changes over time. In the United States, marriages between Protestants and Catholics were once taboo, but they are not widely opposed now. Traditional, Folk, and Indigenous Cultures With the beginning of the Industrial Revolution in the late 18th century, modern transportation and communication connected people as never before and led to extensive cultural mixing, especially as cities have grown. The world prior to this time was very different; however, remnants of the past are still evident in our modern cultures. Traditional, folk, and indigenous cultures share some important characteristics and are often grouped together, but they do have some subtle differences. Traditional Culture Recently, the meanings of traditional, folk, and indigenous culture have begun to merge, causing geographers to debate when each should be used. Increasingly, the term traditional culture is used to encompass all three cultural designations. All three types share the function of passing down long-held beliefs, values, and practices and are generally resistant to rapid changes in their culture. Folk Culture The beliefs and practices of small, homogenous groups of people, often living in rural areas that are relatively isolated and slow to change, are known as folk cultures. Like all cultures, they demonstrate the diverse ways that people have adapted to a physical environment. For example, people around the world learned to make shelters out of available resources, whether 3.1: INTRODUCTION TO CULTURE 133 it was snow or mud bricks or wood. However, people used similar resources such as wood differently. In Scandinavia, people used trees to build cabins. In the American Midwest, people processed trees into boards, built a frame, and attached the boards to it. Many traits of folk culture continue today. Corn was first grown in Mexico around 10,000 years ago, and it is still grown there today. While many elements of folk culture exist side by side with modern culture, there are people whose societies have changed little, if at all, from long ago. These people practice traditional cultures, those which have not been affected by modern technology or influences. They often live in remote regions, such as some small tribes in the Amazon rainforest, and have scant knowledge of the outside world. As the lines continue blurring between cultural designations, the Amish of Pennsylvania are often referenced as both folk and traditional culture. Indigenous Culture When members of an ethnic group reside in their ancestral lands, and typically possess unique cultural traits, such as speaking their own exclusive language, they are considered an indigenous culture. Some indigenous peoples have been displaced from their native lands, but still practice their indigenous culture. Native Americans in the United States, such as the Navajo, have kept indigenous cultural practices. First Nations of Canada, such as the Inuit, have also retained their indigenous culture. Globalization and Popular Culture As a result of the Industrial Revolution, improvements in transportation and communication have shortened the time required for movement, trade, or other forms of interaction between two places. This development, known as space-time compression (see Topics 1.4 and 3.6), has accelerated culture change around the world. In 1817, a freight shipment from Cincinnati needed 52 days to reach New York City. By 1850, because of canals and railroads, it took half that long. And by 1852, it took only 7 days. Today, an airplane flight takes only a few hours, and digital information takes seconds or less. Similar change has occurred on the global scale. People travel freely across the world in a matter of hours, and communication has advanced to a point where people share information instantaneously across the globe. The increased global interaction has had a profound impact on cultures, from spreading English across the world to instant sharing of news, events and music. Globalization specifically refers to the increased integration of the world economy since the 1970s. The process of intensified interaction among peoples, governments, and companies of different countries around the globe has had profound impacts on culture. The culture of the United States is intertwined with globalization. Through the influence of its corporations, Hollywood movies, and government, the United States exerts widespread influence in other countries. But other countries also shape American culture. For example, in 2019, the National Basketball Association included players from 38 countries or territories. When cultural traits- such as clothing, music, movies, and types of 134 HUMAN GEOGRAPHY: AP. EDITION businesses-spread quickly over a large area and are adopted by various groups, they become part of popular culture. Elements of popular culture often begin in urban areas and diffuse quickly through globalization processes such as the media and Internet. These elements can quickly be adopted worldwide, making them part of global culture. People around the world follow European soccer, Indian Bollywood movies, and Japanese animation known as anime. With people in many nations wearing similar clothes, listening to similar music, and eating similar food, popular cultural traits often promote uniformity in beliefs, values, and the cultural landscape across many places The cultural landscape, also known as the built environment (see Topic 3.2), is the modification of the environment by a group and is a visible reflection of that group's cultural beliefs and values. Traditional Culture to Popular Culture Popular culture emphasizes trying what is new rather than preserving what is traditional. Many people, especially older generations or those who follow a folk culture, openly resist the adoption of popular cultural traits. They do this by preserving traditional languages, religions, values, and foods. While older generations often resist the adoption of popular culture, they seldom are successful in keeping their traditional cultures from changing, especially among the young people of their society. One clash between popular and traditional culture is occurring in Brazil. As the population expands to the interior of the rain forest, many indigenous cultures, like the Yanamamo tribe, have more contact with outside groups. Remaining isolated by the forest is becoming increasingly difficult as many young people from the indigenous cultures become exposed to popular culture and begin to integrate into the larger Brazilian society. As the young people leave their communities, they are more likely to accept popular culture at the expense of their indigenous cultural heritage, which threatens the very existence of their folk culture. Traditional culture typically exhibits horizontal diversity, meaning each traditional culture has its own customs and language that makes it distinct from other culture groups. Yet, people people within each group are usually homogeneous, or very similar to each other. By contrast, popular culture typically exhibits vertical diversity, meaning that modern urban societies are usually heterogeneous, or exhibiting differences, within the society and usually contain numerous multiethnic neighborhoods. However, on a global scale popular cultures are relatively similar with the same type of malls, shops, fast food, and clothing. Urban global culture centers are not identical, yet, global cities often do not have as much horizontal diversity across space as folk cultures. 3.1: INTRODUCTION TO CULTURE 135 COMPARING TRADITIONAL AND POPULAR CULTURE Trait Traditional Culture Popular or Global Culture Society • Rural and isolated location • Urban and connected location • Homogeneous and • Diverse and multiethnic indigenous population population • Most people speak an • Many people speak a global indigenous or ethnic local language such as English or language Arabic • Horizontal diversity • Vertical diversity Social • Emphasis on community and • Emphasis on individualism and Structure conformity making choices • Families live close to each • Dispersed families other • Weakly defined gender roles • Well-defined gender roles Diffusion • Relatively slow and limited • Relatively rapid and extensive • Primarily through relocation • Often hierarchical • Oral traditions and stories • Social media and mass media Buildings and • Materials produced locally, • Materials produced in distant Housing such as stone or grass factories, such as steel or glass • Built by community or owner • Built by a business • Similar style for community • Variety of architectural styles • Different between cultures • Similar between cities • Traditional architecture • Postmodern / contemporary architecture Food • Locally produced • Often imported • Choices limited by tradition • Wide range of choice • Prepared by the family or • Purchased in restaurants community Spatial Focus • Local and regional • National and global Artifacts, Mentifacts, and Sociofacts Whether a cultural attribute is considered traditional, folk, indigenous, or popular in nature, it is valuable to differentiate between elements of culture that can be seen and those that can not. There are artifacts that comprise the material culture, which consists of tangible things, or those that can be experienced by the senses. Art, clothing, food, music, sports, and housing types are all tangible elements of culture. Another element of the study of artifacts is understanding the techniques to use or build a specific artifact. Artifacts can be unique to a particular culture, or can be shared. For example, people of all cultures need to communicate through language, yet there are many groups that possess languages unique to their culture. The ability to read, write and understand the English language is an artifact of importance for much of popular global culture. 136 HUMAN GEOGRAPHY: AP" EDITION Mentifacts comprise a group's nonmaterial culture and consist ofintangible concepts, or those not having a physical presence. Beliefs, values, practices, and aesthetics (pleasing in appearance) determine what a cultural group views as acceptable and desirable. Mentifacts can also be unique or shared. People of many cultures possess an belief in one or many deities, and often the deities are unique to that culture. The belief in a god is a mentifact-the religious building or symbols are artifacts. Cultural groups also possess sociofacts, which are the ways people organize their society and relate to one another. Taken altogether, people tend to see the whole of their culture as greater than the sum of its individual parts. Sociofacts are embodied through families, governments, sports teams, religious organizations, education systems, and other social constructs. As with artifacts and mentifacts, sociofacts may also be unique or similar to other societies. Families are the foundations of most societies, yet what constitutes the structure of a family may vary widely between cultural groups. For example, Western cultures tend to view the nuclear family, consisting of the parents and their children as the basic family unit. By contrast, in many Western African cultures the norm is the extended family, consisting of several generations and other family members such as cousins living under one roof.

What is a Plant Cell? Plant cells are eukaryotic cells that vary in several fundamental factors from other eukaryotic organisms. Both plant and animal cells contain a nucleus along with similar organelles. One of the distinctive aspects of a plant cell is the presence of a cell wall outside the cell membrane. Plant Cell Structure Just like different organs within the body, plant cell structure includes various components known as cell organelles that perform different functions to sustain itself. These organelles include: Cell Wall It is a rigid layer which is composed of polysaccharides cellulose, pectin and hemicellulose. It is located outside the cell membrane. It also comprises glycoproteins and polymers such as lignin, cutin, or suberin. The primary function of the cell wall is to protect and provide structural support to the cell. The plant cell wall is also involved in protecting the cell against mechanical stress and providing form and structure to the cell. It also filters the molecules passing in and out of it. The formation of the cell wall is guided by microtubules. It consists of three layers, namely, primary, secondary and the middle lamella. The primary cell wall is formed by cellulose laid down by enzymes. Cell membrane It is the semi-permeable membrane that is present within the cell wall. It is composed of a thin layer of protein and fat. The cell membrane plays an important role in regulating the entry and exit of specific substances within the cell. For instance, cell membrane keeps toxins from entering inside, while nutrients and essential minerals are transported across. Nucleus The nucleus is a membrane-bound structure that is present only in eukaryotic cells. The vital function of a nucleus is to store DNA or hereditary information required for cell division, metabolism and growth. 1. Nucleolus: It manufactures cells’ protein-producing structures and ribosomes. 2. Nucleopore: Nuclear membrane is perforated with holes called nucleopore that allow proteins and nucleic acids to pass through. Plastids They are membrane-bound organelles that have their own DNA. They are necessary to store starch and to carry out the process of photosynthesis. It is also used in the synthesis of many molecules, which form the building blocks of the cell. Some of the vital types of plastids and their functions are stated below: Leucoplasts They are found in the non-photosynthetic tissue of plants. They are used for the storage of protein, lipid and starch. Chromoplasts They are heterogeneous, colored plastid which is responsible for pigment synthesis and for storage in photosynthetic eukaryotic organisms. Chromoplasts have red-, orange- and yellow-colored pigments which provide color to all ripe fruits and flowers. Central Vacuole It occupies around 30% of the cell’s volume in a mature plant cell. Tonoplast is a membrane that surrounds the central vacuole. The vital function of the central vacuole apart from storage is to sustain turgor pressure against the cell wall. The central vacuole consists of cell sap. It is a mixture of salts, enzymes and other substances. Golgi Apparatus They are found in all eukaryotic cells, which are involved in distributing synthesized macromolecules to various parts of the cell. Ribosomes They are the smallest membrane-bound organelles which comprise RNA and protein. They are the sites for protein synthesis, hence, also referred to as the protein factories of the cell. Mitochondria They are the double-membraned organelles found in the cytoplasm of all eukaryotic cells. They provide energy by breaking down carbohydrate and sugar molecules, hence they are also referred to as the “Powerhouse of the cell.” Lysosome Lysosomes are called suicidal bags as they hold digestive enzymes in an enclosed membrane. They perform the function of cellular waste disposal by digesting worn-out organelles, food particles and foreign bodies in the cell. In plants, the role of lysosomes is undertaken by the vacuoles. Chloroplasts It is an elongated organelle enclosed by phospholipid membrane. The chloroplast is shaped like a disc and the stroma is the fluid within the chloroplast that comprises a circular DNA. Each chloroplast contains a green colored pigment called chlorophyll required for the process of photosynthesis. The chlorophyll absorbs light energy from the sun and uses it to transform carbon dioxide and water into glucose. Structure of Chloroplast Chloroplasts are found in all higher plants. It is oval or biconvex, found within the mesophyll of the plant cell. The size of the chloroplast usually varies between 4-6 µm in diameter and 1-3 µm in thickness. They are double-membrane organelle with the presence of outer, inner and intermembrane space. There are two distinct regions present inside a chloroplast known as the grana and stroma. • Grana are made up of stacks of disc-shaped structures known as thylakoids or lamellae. The granum of the chloroplast consists of chlorophyll pigments and are the functional units of chloroplasts. • Stroma is the homogenous matrix which contains grana and is similar to the cytoplasm in cells in which all the organelles are embedded. Stroma also contains various enzymes, DNA, ribosomes, and other substances. Stroma lamellae function by connecting the stacks of thylakoid sacs or grana. The chloroplast structure consists of the following parts: Membrane Envelope It comprises inner and outer lipid bilayer membranes. The inner membrane separates the stroma from the intermembrane space. Intermembrane Space The space between inner and outer membranes. Thylakoid System (Lamellae) The system is suspended in the stroma. It is a collection of membranous sacs called thylakoids or lamellae. The green colored pigments called chlorophyll are found in the thylakoid membranes. It is the sight for the process of light-dependent reactions of the photosynthesis process. The thylakoids are arranged in stacks known as grana and each granum contains around 10-20 thylakoids. Stroma It is a colorless, alkaline, aqueous, protein-rich fluid present within the inner membrane of the chloroplast present surrounding the grana. Grana Stack of lamellae in plastids is known as grana. These are the sites of conversion of light energy into chemical energy. Chlorophyll It is a green photosynthetic pigment that helps in the process of photosynthesis. Functions of Chloroplast Following are the important chloroplast functions: • The most important function of the chloroplast is to synthesize food by the process of photosynthesis. • Absorbs light energy and converts it into chemical energy. • Chloroplast has a structure called chlorophyll which functions by trapping the solar energy and is used for the synthesis of food in all green plants. • Produces NADPH and molecular oxygen (O 2 ) by photolysis of water. • Produces ATP – Adenosine triphosphate by the process of photosynthesis. • The carbon dioxide (CO2) obtained from the air is used to generate carbon and sugar during the Calvin Cycle or dark reaction of photosynthesis. Mitochondria “Mitochondria are membrane-bound organelles present in the cytoplasm of all eukaryotic cells, that produce adenosine triphosphate (ATP), the main energy molecule used by the cell.” What are Mitochondria? Popularly known as the “Powerhouse of the cell,” mitochondria (singular: mitochondrion) are a double membrane-bound organelle found in most eukaryotic organisms. They are found inside the cytoplasm and essentially function as the cell’s “digestive system.” They play a major role in breaking down nutrients and generating energy-rich molecules for the cell. Many of the biochemical reactions involved in cellular respiration take place within the mitochondria. The term ‘mitochondrion’ is derived from the Greek words “mitos” and “chondrion” which means “thread” and “granules-like”, respectively. It was first described by a German pathologist named Richard Altmann in the year 1890. Structure of Mitochondria • The mitochondrion is a double-membraned, rod-shaped structure found in both plant and animal cell. • Its size ranges from 0.5 to 1.0 micrometers in diameter. • The structure comprises an outer membrane, an inner membrane, and a gel-like material called the matrix. • The outer membrane and the inner membrane are made of proteins and phospholipid layers separated by the intermembrane space. • The outer membrane covers the surface of the mitochondrion and has a large number of special proteins known as porins. Cristae The inner membrane of mitochondria is rather complex in structure. It has many folds that form a layered structure called cristae, and this helps in increasing the surface area inside the organelle. The cristae and the proteins of the inner membrane aid in the production of ATP molecules. The inner mitochondrial membrane is strictly permeable only to oxygen and ATP molecules. A number of chemical reactions take place within the inner membrane of mitochondria. Mitochondrial Matrix The mitochondrial matrix is a viscous fluid that contains a mixture of enzymes and proteins. It also comprises ribosomes, inorganic ions, mitochondrial DNA, nucleotide cofactors, and organic molecules. The enzymes present in the matrix play an important role in the synthesis of ATP molecules. Functions of Mitochondria The most important function of mitochondria is to produce energy through the process of oxidative phosphorylation. It is also involved in the following process: 1. Regulates the metabolic activity of the cell 2. Promotes the growth of new cells and cell multiplication 3. Helps in detoxifying ammonia in the liver cells 4. Plays an important role in apoptosis or programmed cell death 5. Responsible for building certain parts of the blood and various hormones like testosterone and estrogen 6. Helps in maintaining an adequate concentration of calcium ions within the compartments of the cell 7. It is also involved in various cellular activities like cellular differentiation, cell signaling, cell senescence, controlling the cell cycle and in cell growth. Disorders Associated with Mitochondria Any irregularity in the way mitochondria function can directly affect human health, but often, it is difficult to identify because symptoms differ from person to person. Disorders of the mitochondria can be quite severe; in some cases, they can even cause an organ to fail.

Factoring the Sum and Difference of Cubes - Exit Quiz

Chapter 8: The Worlds of North and South Geography Geography refers to the seasons, climate, soil, and physical features of a region (mountains, rivers, etc.) The differences in geography b/t the N and S is one of the major reasons slavery b/c entrenched in the S while it died out in the N. Geography of the North The N has diverse geography and experiences four distinct seasons including long, harsh winters. The Great Plains region has some of the best farmland in the country. New England has rocky, hilly wilderness, not well suited for farming. It has hundreds of bays and harbors along its coastline. States farther S had rich soil and coastal access through rivers. The N also experienced mass deforestation b/c of the need for lumber and to make room for farms. Geography of the South Climate: the S had mild winters, and a long, hot, humid growing season. It has fertile lowlands, marshes and swamps. It's ideal for growing tobacco, sugar, rice, indigo, and cotton (cash crops). B/c of the geography of the S, their whole way of life was based on agriculture and geography is one of the major reasons why slavery took off in the S. Economies Economy basically refers to the way people make and spend money. The Northern economy was far more diversified than the Southern. Economy of the North The North experienced the Industrial Revolution—the shift from handmade goods to machine-made goods. This resulted in new jobs, increased production, and improved efficiency in agriculture. IOW, you can make things faster, easier, and cheaper. More ppl get more stuff. Factories were almost always located next to rivers. The Reaper The Indust. Rev. changed northern agriculture with Cyrus McCormick’s reaper. It could cut 28xs more grain than a single man. The Sewing Machine Elias Howe's sewing machine; At 250 stitches a minute, Howe's lockstitch mechanism out-stitched the output of five hand seamstresses with a reputation for speed, completing in one hour what took the sewers 14.5 hours. The Textile Mill Francis Cabot Lowell's textile mill: essentially the first factory in the US, Lowell set the model for all future factories. Interchangeable Parts Eli Whitney's interchangeable parts; considered the "dawning of a new age" of machinery. This concept was applied to pretty much all manufacturing. Economy of the South The South's economy was based on AGRICULTURE. Most southerners were agrarians. Most had small farms, some owned plantations. Slavery beginning to decline in late 1700s; prices went down (tobacco, indigo) and cotton was difficult. King Cotton Cotton was South’s most important crop. Earned more money than all other exports combined. The S would go on to supply 75% of the world's cotton demand. Cotton Gin Eli Whitney invented the cotton gin in 1794 and forever changed the US. The gin made cotton incredibly profitable. We start to see the effects of the cotton gin around 1820. Slavery and Cotton Southerners put all their money into slaves and land, and almost none into building factories. With the spread of cotton, demand for slaves increased. 1790 to 1850, number of slaves rose 600%. Transportation Again, the N was far more inventive in their approach to transportation than the S. Transportation in the North National Road National Road stretched from the East (the Potomac), over the Appalachians, to the West (Illinois), over 620 miles. Steamboat In 1807, Robert Fulton invented the steamboat. It traveled 150 miles UP the Hudson River at a speed of 5 mph. Erie Canal Built b/t 1817 and 1825, the canal spanned 363 miles and connected Lake Erie to the Hudson River. This connected farms in the W to cities in the E and the Atlantic Ocean. Clipper Ship Clippers were narrow w massive sails that were built for speed. They cut the time it took to cross the Atlantic in half. Locomotive The fastest and cheapest way to move goods was by steam-powered trains. The first RR was the B&O which was built in 1827. Transportation in the South Most people and goods in the South traveled by rivers in steamboats. The South had trains, but less than half the amount of railroad track than the North had. Society (The People) The people who made up the N and S could not have been more different. The S was primarily agrarian while the N was b/c urbanized. The S was holding on to the past, while the N was embracing change. Society in the South Society was organized into 3 distinct classes of people: rich plantation owners at the top; then white farmers and workers; slaves on the bottom. This rigid social class system was the result of a slave-based agricultural system. Power Structure Only 1 in 4 whites owned a slave. Plantation owners, who owned more than 20 slaves, dominated politics and the economy. Society in the North 7 of 10 Northerners still lived on farms by the 1840s (6 of 10 by 1860), but urbanization was growing fast in the N. The N relied on wage labor as opposed to slave labor, so most blacks in the N were free. N blacks were not treated equally and the N was about as racist as the S. Immigration Compared to the S, the N population was exploding, in large part bc of immigration. Between 1845 and 1860, 4 million immigrants came to the North. Most were German and Irish. Irish--a potato famine; German--a failed revolution. Ethnic neighborhoods developed as a result.

Related quizzes

Related quizzes