Algebra 10.7 Factoring Special Products Use the Patterns! First and last terms are perfect squares! (2x + 3)2 4x² + 12x + 9 Perfect Square Trinomial! The middle term is twice the product of the square roots of the first and third terms. (2p - 4) (2p + 4) 4p² - 16 Difference of two squares (DTS)! The difference of… two squares! First and last terms are perfect squares! (2x - y)2 4x² - 4xy + y² Perfect Square Trinomial! The middle term is twice the product of the square roots of the first and third terms. The key is to recognize when you see a perfect square trinomial or a DTS! Factoring Patterns! First and last terms are perfect squares! a² + 2ab + b2 Perfect Square Trinomial! (a + b)2 The middle term is twice the product of the square roots of the first and third terms. a² - b2 Difference of two squares (DTS)! (a - b)(a + b) The difference of… two squares! First and last terms are perfect squares! a² - 2ab + b² Perfect Square Trinomial! (a - b)2 The middle term is twice the product of the square roots of the first and third terms. The key is to recognize when you see a perfect square trinomial or a DTS! Factor! 2x²- 18 2(x²- 9) 2(x + 3)(x – 3) 49t²- ¼r2 (7t + ½r)(7t – ½r) DTS! DTS! 81x²- 25y² (9x – 5y)(9x + 5y) DTS! 27x²- 12 3(9x²- 4) DTS! 3(3x + 2)(3x – 2) Factor! -3x²- 18x - 27 -3(x²+ 6x + 9) Perfect Square Trinomial! 9y²- 60y + 100 -3(x + 3)2 (3y – 10)2 Perfect Square Trinomial! 2x²- 12x + 18 2(x²- 6x + 9) 2(x – 3)2 49x²+ 84x + 36 (7x + 6)2 Perfect Square Trinomial! Perfect Square Trinomial! Solve! 3x²- 30x = -75 3x²- 30x + 75 = 0 x²- 10x + 25 = 0 Divide each side by 3! (x – 5)2 = 0 x= 5 Perfect Square Trinomial! 36y²- 121 = 0 DTS! -6x²+ 8x + 14 = 0 3x²- 4x – 7 = 0 Divide each side by -2! (6y + 11)(6y – 11) = 0 y = 11/6, -11/6 (x + 1 )(3x - 7) = 0 x = -1, 7/3 Solve! 4x²- 1 = 0 DTS! 7x²- 10x = -3 7x²- 10x + 3 = 0 32x²- 80x + 50 = 0 16x²- 40x + 25 = 0 Divide each side by 2! Perfect Square Trinomial! (2x + 1)(2x – 1) = 0 x = ½, -½ (7x – 3 )(x – 1) = 0 x = 1, 3/7 (4x – 5)2 = 0 x = 5/4 HW • P. 622-624 (#19-61, 83-93) Odds Maybe factor out instead of divide each side by GCF as it applies to Ch 11