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```					          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(x + 3)(x – 3)
2(x²- 9)  DTS!

49t²- ¼r2              (7t + ½r)(7t – ½r)
DTS!

81x²- 25y²              (9x – 5y)(9x + 5y)
DTS!

27x²- 12                3(3x + 2)(3x – 2)
3(9x²- 4)
DTS!
Factor!

-3x²- 18x - 27                               -3(x + 3)2
-3(x²+ 6x + 9)
Perfect Square Trinomial!

9y²- 60y + 100                               (3y – 10)2
Perfect Square Trinomial!

2x²- 12x + 18                                2(x – 3)2
2(x²- 6x + 9)
Perfect Square Trinomial!

49x²+ 84x + 36                               (7x + 6)2
Perfect Square Trinomial!
Solve!
3x²- 30x = -75                                  (x – 5)2 = 0
3x²- 30x + 75 = 0                                 x= 5
x²- 10x + 25 = 0
Divide each side by 3!

Perfect Square Trinomial!

36y²- 121 = 0                              (6y + 11)(6y – 11) = 0
y = 11/6, -11/6
DTS!

-6x²+ 8x + 14 = 0
Divide each side by -2!
(x + 1 )(3x - 7) = 0
3x²- 4x – 7 = 0                                  x = -1, 7/3
Solve!
4x²- 1 = 0                                    (2x + 1)(2x – 1) = 0
DTS!
x = ½, -½

7x²- 10x = -3                                       (7x – 3 )(x – 1) = 0
7x²- 10x + 3 = 0                                       x = 1, 3/7

32x²- 80x + 50 = 0
Divide each side by 2!
(4x – 5)2 = 0
16x²- 40x + 25 = 0                                    x = 5/4
Perfect Square Trinomial!
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

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