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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 68 Page 84

The formula to factor the difference of two squares is a^2-b^2=(a+b)(a-b).

3(x+1)(x-1)

Practice makes perfect

To factor the given expression, we will first identify and factor out the greatest common factor. Then, we will use the formula for the difference of two squares.

Factor Out the GCF

The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 3.

3x^2-3

SplitIntoFactors

Split into factors

3* x^2- 3* 1

Factor out 3

3(x^2-1)

Difference of Squares

Look closely at the expression x^2-1. It can be expressed as the difference of two perfect squares.

x^2-1

Write as a power

x^2-1^2

Recall the formula to factor a difference of squares. a^2- b^2 ⇔ ( a+ b)( a- b) We can apply this formula to our expression. 3 ( x^2- 1^2 ) ⇔ 3( x+ 1)( x- 1)

Checking Our Answer

Check your answer ✓

We can apply the Distributive Property and compare the result with the given expression.

3 (x + 1) (x - 1)

Distribute 3

(3x + 3) (x - 1)

Distribute (x-1)

3 x (x - 1) + 3 ( x - 1)

Distribute 3x

3x^2 -3x + 3 ( x - 1)

Distribute 3

3x^2 -3x + 3x - 3

Subtract term

3x^2-3

After applying the Distributive Property and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!

Subchapter links

1 Adding and Subtracting Polynomials p.81

2 Multiplying a Polynomial by a Monomial p.81

3 Multiplying Polynomials p.81

4 Special Products p.82

5 Using the Distributive Property p.82

6 Solving x^2+bx+c=0 p.83

7 Solving ax^2+bx+c=0 p.83

8 Differences of Squares p.84

9 Perfect Squares p.84

10 Roots and Zeros p.85