1. Algebra 10.7 Factoring Special Products

2. Use the Patterns! (2x + 3) 2 (2p - 4) (2p + 4) (2x - y) 2 4x² + 12x + 9 4p² - 16 4x² - 4xy + y² Perfect Square Trinomial! Difference of two squares (DTS)! Perfect Square Trinomial! First and last terms are perfect squares! The middle term is twice the product of the square roots of the first and third terms. First and last terms are perfect squares! The middle term is twice the product of the square roots of the first and third terms. two squares!The difference of… The key is to recognize when you see a perfect square trinomial or a DTS!

3. Factoring Patterns! (a + b) 2 (a - b)(a + b) (a - b) 2 a² + 2ab + b 2 a² - b 2 a² - 2ab + b² Perfect Square Trinomial! Difference of two squares (DTS)! Perfect Square Trinomial! First and last terms are perfect squares! The middle term is twice the product of the square roots of the first and third terms. First and last terms are perfect squares! The middle term is twice the product of the square roots of the first and third terms. two squares!The difference of… The key is to recognize when you see a perfect square trinomial or a DTS!

4. Factor! 2(x + 3)(x – 3) (7t + ½r)(7t – ½r) (9x – 5y)(9x + 5y) 3(3x + 2)(3x – 2) 2x²- 18 49t²- ¼r 2 81x²- 25 y² 27x²- 12 2(x²- 9) 3(9x²- 4) DTS!

5. Factor! -3(x + 3) 2 (3y – 10) 2 2(x – 3) 2 (7x + 6) 2 -3x²- 18x - 27 9y²- 60y + 100 2x²- 12 x + 18 49x²+ 84x + 36 -3(x²+ 6x + 9) 2(x²- 6 x + 9) Perfect Square Trinomial!

6. Solve! (x – 5) 2 = 0 (6y + 11)(6y – 11) = 0 (x )(3x ) = 0 3x²- 30x = -75 36y²- 121 = 0 -6x²+ 8 x + 14 = 0 3x²- 30x + 75 = 0 3x²- 4 x – 7 = 0 x²- 10x + 25 = 0 Divide each side by 3! x = 5 y = 11/6, -11/6 Divide each side by -2! x = -1, 7/3 Perfect Square Trinomial! DTS! 1 7 + -

7. Solve! (2x + 1)(2x – 1) = 0 (7x )(x ) = 0 (4x – 5) 2 = 0 4x²- 1 = 0 7x²- 10x = -3 32x²- 80 x + 50 = 0 16x²- 40 x + 25 = 0 x = ½, -½ x = 1, 3/7 Divide each side by 2! x = 5/4 7x²- 10x + 3 = 0 DTS! Perfect Square Trinomial! – 3 1

8. 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