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