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Factoring Special Forms
Chapter 5 Section 5 Factoring Special Forms
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Factoring Difference of Two Squares
Two ways Area model Rule
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Factor 9x Area model: set up 9x2 – 100 9x2 + 0x – 100 Sum is 0, product is Two numbers are 30 and - 30
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Factor 9x Rewrite as the difference of two squares 9x2 is (3x)2 100 is 102 So (3x) Rule: Factor the difference of two square as the product of the sum and difference of the those terms. Thus: (3x – 10)(3x+ 10)
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Caution Be sure that you factor the common factor before factoring
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Try 4x2 – 9 2x3 – 8x
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Repeated Factorization
Try: 81x4 – 16 Note: After you factor, look at the factors.
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Factoring Perfect Square Trinomials
Two ways Area Model Rule
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Check for a Perfect Square Trinomial
Middle (linear) term is twice the product of the outside terms that are being squared. Example: 4x2 + 12xy + 9y2 leading term: (2x)2 Last term: (3y)2 Multiply the expression being square and multiply by 2 2(2x)(3y) which is the middle term.
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Factor: 4x2 + 12xy + 9y2 Since it is a perfect square trinomial
Factor: Take the terms being squared in order and write as a binomial with the first sign and square the binomial. (2x + 3y)2
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Factor: 4x2 + 12xy + 9y2 Set up for the area model
Sum is 12, product is (4)(9) Numbers are 6xy and 6xy
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Sum or Difference of Two Cube
Observe: (A + B)3 = (A + B)(A2 - AB + B2) (A - B)3 = (A - B)(A2 + AB + B2) Words: Write the binomial, then square the first, change the signs, multiply together and square the second.
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Factor: x Rewrite as the sum of cubes (x)3 + (5)3
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Try 25x4 – 25y6 2x3y – 18xy 25y2 – 10y + 1 27x3 - 8
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Summary Binomial Trinomial Difference of two squares
Sum or Difference of two cubes Trinomial Area model Grouping Perfect square trinomial
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