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Algebra. 10.7 Factoring Special Products. Use the Patterns!. First and last terms are perfect squares!. 4x² + 12x + 9. (2x + 3) 2. Perfect Square Trinomial!. The middle term is twice the product of the square roots of the first and third terms. 4p² - 16.

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algebra

Algebra

10.7 Factoring Special Products

use the patterns
Use the Patterns!

First and last terms are perfect squares!

4x² + 12x + 9

(2x + 3)2

Perfect Square Trinomial!

The middle term is twice the product of the square roots

of the first and third terms.

4p² - 16

(2p - 4) (2p + 4)

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
Factoring Patterns!

First and last terms are perfect squares!

a² + 2ab + b2

(a + b)2

Perfect Square Trinomial!

The middle term is twice the product of the square roots

of the first and third terms.

a² - b2

(a - b)(a + b)

Difference of two squares (DTS)!

The difference of…

two squares!

First and last terms are perfect squares!

a² - 2ab + b²

(a - b)2

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!

factor
Factor!

2x²- 18

2(x + 3)(x – 3)

2(x²- 9)

DTS!

(7t + ½r)(7t – ½r)

49t²- ¼r2

DTS!

81x²- 25y²

(9x – 5y)(9x + 5y)

DTS!

27x²- 12

3(3x + 2)(3x – 2)

3(9x²- 4)

DTS!

factor1
Factor!

-3x²- 18x - 27

-3(x + 3)2

-3(x²+ 6x + 9)

Perfect Square Trinomial!

(3y – 10)2

9y²- 60y + 100

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
Solve!

(x – 5)2 = 0

3x²- 30x = -75

3x²- 30x + 75 = 0

x= 5

Divide each side by 3!

x²- 10x + 25 = 0

Perfect Square Trinomial!

(6y + 11)(6y – 11) = 0

36y²- 121 = 0

y= 11/6, -11/6

DTS!

-6x²+ 8x + 14 = 0

(x )(3x ) = 0

+ -

1 7

Divide each side by -2!

3x²- 4x – 7 = 0

x= -1, 7/3

solve1
Solve!

(2x + 1)(2x – 1)= 0

4x²- 1 = 0

x= ½, -½

DTS!

(7x )(x ) = 0

– –

3 1

7x²- 10x = -3

7x²- 10x + 3 = 0

x= 1, 3/7

32x²- 80x + 50 = 0

(4x – 5)2 = 0

Divide each side by 2!

16x²- 40x + 25 = 0

x= 5/4

Perfect Square Trinomial!

slide8
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