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Warmups – factor. 1) Write the prime factorization: 224 2) x2 +19x + 18 3) 49y2 + 56y + 16 4) 5xy + 15x + 4y + 12 10-4 Factoring Difference of Squares Objective: To identify and factor binomials that are the difference of two squares. Standard 11.0 Remember… a 2ab b ( a b) a 2ab b ( a b) 2 2 2 2 2 2 Do you remember…. (a b)(a b) So…. a b 2 2 a b (a b)(a b) 2 2 Recognizing a Difference of Squares m 81 2 1st term is a perfect square 2nd term is a perfect square Subtraction Answer… ( 1st 2nd )( 1st 2nd ) Example 1: Factor. 9 x 49 2 (3 x 7)(3 x 7) LTT: IS IT A DIFFERENCE OF SQUARES? If so… factor it. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) x2 – 4 9x2 – 1 2x2 – 4 2x2 – 8 x2 + y2 x3 – 25 9xy – y2 -16 + x2 -4 – 16x2 x4 – 81 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) YES -------------- YES -------------- NO √2 YES 2(x2 – 4) - NO Adding NO x3 NO x YES x2 – 16 --- NO -(4 + 16x2) YES √x4 = x2 --- Example 2 20cd 2 125c5 1. Factor out the GCF: 5c 2. Rewrite the polynomial: 5c(4d 25c ) 2 4 3. Factor the difference of squares inside of the parenthesis: 2 2 5c(2d 5c )(2d 5c ) 4. Don’t forget about the GCF on the outside TOO: Factor 1) 25x2 – 121 2) 16x4 – y2 3) -98 + 2x2 4) 4x2 – 9y2 5) 3x3 – 12x Factor & List which process(es) you used. GCF Grouping X-Box Perfect Square Trinomial Difference of Squares y 6 y 16 2 24m 8 2 16 x 40 x 24 2 81x 16 y 4 4 n 2n 3mn 6m 2 Factor & List which process(es) you used. GCF Grouping X-Box Perfect Square Difference of Squares 15 x 45 y 2 2 1 8 p 16 p 2 t t t 1 3 2 4a 8a 4a 3 2 2 x 3x 5 x 3 2 Homework Pg. 584 #22-39 all