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Factor Special Products April 4, 2014 Pages 600-602

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Factor the polynomial. 1. y 2 – 16 = (y + 4)(y – 4) 2. 25m 2 – 36 = (5m + 6)(5m – 6) 3. x 2 – 49y 2 = (x + 7y)(x – 7y) Write as a 2 – b 2. Difference of two squares pattern Write as a 2 – b 2. Difference of two squares pattern Write as a 2 – b 2. Difference of two squares pattern = y 2 – 4 2 = (5m) 2 – 6 2 = x 2 – (7y) 2

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4. 8 – 18n 2 = 2(4 – 9n 2 ) = 2[2 2 – (3n) 2 ] = 2(2 + 3n)(2 – 3n) Factor out common factor. Write 4 – 9n 2 as a 2 – b 2. Difference of two squares pattern 5. 4y 2 – 64 = (2y + 8)(2y – 8) Write as a 2 – b 2. Difference of two squares pattern = (2y) 2 – (8) 2

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Perfect Square Trinomial Pattern a 2 + 2ab + b 2 = (a + b) 2 a 2 – 2ab + b 2 = (a – b) 2

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6.n 2 – 12n + 36= n 2 – 2(n 6) + 6 2 Write as a 2 – 2ab + b 2. = (n – 6) 2 Perfect square trinomial pattern 7.7. 9x 2 – 12x + 4 Write as a 2 – 2ab + b 2. = ( 3x – 2) 2 Perfect square trinomial pattern 8.8. 4s 2 + 4st + t 2 = (2s) 2 + 2(2s t) + t 2 Write as a 2 + 2ab + b 2. = (3x) 2 – 2(3x 2) + 2 2 = (2s + t) 2 Perfect square trinomial pattern Factor the polynomial.

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9. – 3y 2 + 36y – 108. – 3y 2 + 36y – 108 Factor out – 3. = – 3 ( y 2 – 2(y 6) + 6 2 ) Write y 2 – 12y + 36 as a 2 – 2ab + b 2. = – 3(y – 6) 2 Perfect square trinomial pattern = – 3(y 2 – 12y + 36)

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= (h + 2) 2 Perfect square trinomial pattern Write as a 2 +2ab+ b 2. 10. h 2 + 4h + 4 11. 2y 2 – 20y + 50 Write as y 2 –10y+25 as a 2 –2ab+b 2. Factor out 2 = 2(y – 5) 2 Perfect square trinomial pattern = 2[y 2 –2(y 5) + 5 2 ] = h 2 +2(h 2) +2 2 = 2(y 2 – 10y +25)

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12. Solve the equation x 2 + + = 0. 2 3 x 1 9 9x2 + 6x + 1 = 09x2 + 6x + 1 = 0 Multiply each side by 9 to get rid of the fractions. (3x) 2 + 2(3x 1) + (1) 2 = 0 Write left side as a 2 + 2ab + b 2. (3x + 1) 2 = 0 Zero- product property x = – 1 3 Solve for x. ANSWER The solution of the equation is –. 1 3

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a 2 + 2(a 3) +(3) 2 = 0 Write left side as a 2 + 2ab + b 2. (a + 3) 2 = 0 Zero-product property Solve for a. Solve the equation 13. a 2 + 6a + 9 = 0 a = – 3 a + 3 = 0 Perfect square trinomial pattern

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w 2 + 2(w 7) +(7) 2 = 0 Write left side as a 2 – 2ab + b 2. (w – 7) 2 = 0 Zero-product property Solve for w. 14. w 2 – 14w + 49 = 0 w = 7 w – 7 = 0 Perfect square trinomial pattern

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Write left side as a 2 – 2ab + b 2. (n + 9) (n – 9) = 0 Zero-product property Solve for w. 15. n 2 – 81= 0 n 2 – 9 2 = 0 (n + 9) = 0(n – 9) = 0 or n = – 9 or n = 9 Difference of two squares pattern

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HOMEWORK Worksheet

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