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Factoring and expanding algebraic expressions
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Algebra 3: Expanding and FactorisingAlgebra 4: Expanding and Factorising Double BracketsExpanding and FactorisingChapter 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.Factoring and multiples Factoring and Solving Quadratic FunctionsFactoring and GCFs (short)Factoring and GCFs