Algebra 1 Common Core Student Edition, Grade 8-9

Recall from Lesson 8-4 that (a + b){a - b) = a 2 - b 2. So you can factor a difference of

tw o squares, a2 - b2, as (a + b){a - b).

| r ^ Key Concep t Factoring a Difference of Two Squares

Algebra For all real numbers a and b:

a2 - b2 = (a + b){a - b)

Examples x2 - 64 = (jc + 8 ) ( x - 8)

25x2 - 36 = (5x + 6)(5x - 6)

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Fa ct o r i n g a D i f f e r en ce o f Tw o Sq u a r e s

What is the factored form of z 2 - 9?

Factor using the rule fo r a

d iffe re n ce o f t w o squares.

Check your answer by

multiplying the factored

form.

Rewrite 9 as a square.

(z + 3)(z - 3) = z 2 - 3z + 3z - 9

= z 2 - 9

z2_9 = 22 _ 32

= (Z + 3)(z - 3)

Go t I t? 3. What is the factored form of each expression?

a. v2 - 100 b. s2- 16

Fact o r i n g a D i f f er en ce o f Tw o Sq u a r e s

What is the factored form of 16x2 - 81?

16x2 - 81 = (4x)2 - 92 Write each term as a square.

= (4x + 9)(4x - 9) Use the rule fo r the difference o f squares.

mmm
When is a term o f the
form a x 2 a perfect
square?
ax 2 is a p e rfe c t square
w h e n a is a p e rfe ct
square. For exam ple,
16 x 2 is a p e rfe c t square
b u t 1 7 x 2 is not.

Go t I t? 4. a. What is the factored form of 25d2 - 64?

b. Reasoning The expression 25d2 + 64 contains two perfect squares. Can

you use the method in Problem 4 to factor it? Explain your reasoning.

c -V

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| Lesson 8-7 Factoring Special Cases

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