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McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

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Exercise 2 Page 60

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

(2a+5)(2a-5)

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Look closely at the expression 4a^2-25. It can be expressed as the difference of two perfect squares.

4a^2-25

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Write as a power

2^2a^2-5^2

ProdPowII

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

(2a)^2-5^2

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. ( 2a)^2- 5^2 ⇔ ( 2a+ 5)( 2a- 5)

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

(2 a + 5) (2 a - 5)

Distr

Distribute 2a + 5

2a (2a + 5) - 5 (2a + 5)

Distr

Distribute 2a

4a^2 + 10 a - 5(2 a + 5)

Distr

Distribute -5

4 a^2 + 10a - 10 a - 25

SubTerm

Subtract term

4 a^2 - 25

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 2 Page 60

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