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McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 66 Page 71

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

(2x+9y)(2x-9y)

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Look closely at the expression 4x^2-81y^2. It can be expressed as the difference of two perfect squares.

4x^2-81y^2

WritePow

Write as a power

2^2x^2-9^2y^2

ProdPowII

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

(2x)^2-(9y)^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. ( 2x)^2-( 9y)^2 ⇔ ( 2x+ 9y)( 2x- 9y)

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

(2x+9y) (2x-9y)

Distr

Distribute 2x+9y

2x(2x+9y)-9y(2x+9y)

Distr

Distribute 2x

4x^2+18xy-9y(2x+9y)

Distr

Distribute -9y

4x^2+18xy-18xy-81y^2

SubTerm

Subtract term

4x^2-81y^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!

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Exercises p.68-71

Exercise 66 Page 71

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