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McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

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Exercise 24 Page 61

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

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

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

x^2-4y^2

WritePow

Write as a power

x^2-2^2y^2

ProdPowII

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

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

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

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

Distr

Distribute (x + 2y)

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

Distr

Distribute x

x^2 + 2 xy - 2y(x + 2y)

Distr

Distribute -2y

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

SubTerm

Subtract term

x^2 - 4y^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.60-63

Exercise 24 Page 61

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