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McGraw Hill Integrated II, 2012 View details

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Exercise 66 Page 84

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

(8+5x)(8-5x)

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Look closely at the expression 64-25x^2. It can be expressed as the difference of two perfect squares.

64-25x^2

WritePow

Write as a power

8^2-5^2x^2

ProdPowII

a^m b^m = (a b)^m

8^2-(5x)^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. ( 8^2-( 5x)^2 ) ⇔ ( 8+ 5x)( 8- 5x)

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

(8+5x) (8-5x)

Distr

Distribute (8-5x)

8(8-5x)+5x(8-5x)

Distr

Distribute 8

64-40x+5x(8-5x)

Distr

Distribute 5x

64-40x+40x-25x^2

SubTerm

Subtract term

64-25x^2

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

Exercise 66 Page 84

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