# algebra-Expansion and Factorization

May 29th, 2015
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Example 3-This trick is VERY useful to be able to master. It’s when you need to add and subtract within the expression in order to make things work out nicely. It’s about repetition, and your ability to recognize things. So in order to develop

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Algebra SkillsWorksheet OneExpansion and FactorizationFactorizedExpandedx(x+y)(x+y)2(x-y)2(x-y)(x+y)(a+b)(c+d)x2 + xyx2 + 2xy + y2x2 - 2xy + y2x2 - y2 (difference of two squares)ac + ad + ad + bdNote that (x-y)2 = (y-x)2 This result becomes very useful when working with absolute values.Example 1Expand (a+b+c)2 (a+b+c)2= a2 + ab + ac + ab + b2 + bc + ac + ac + bc + c2= a2 + b2 + c2 + 2(ab + bc + ac)Example 2Factorise (x-y)Since a2 - b2 = (a-b)(a+b)Letting x = a2y = b2Then x-y = (?x - ?y)( (?x + ?y)Example 3This trick is VERY useful to be able to master. It's when you need to add and subtract within the expression in order to make things work out nicely. It's about repetition, and your ability to recognize things. So in order to develop these, you'll need to put in hours of maths to open your mind.Factorize x4 + x2 + 1.x4 + x2 + 1= (x4 + 2x2

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