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McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

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Exercise 37 Page 61

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

(a+7)(a-7)

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Look closely at the expression a^2-49. It can be expressed as the difference of two perfect squares.

a^2-49

WritePow

Write as a power

a^2-7^2

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. a^2- 7^2 ⇔ ( a+ 7)( a- 7)

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

(a + 7) (a - 7)

Distr

Distribute a + 7

a(a + 7) - 7 (a + 7)

Distr

Distribute a

a^2 + 7 a - 7(a + 7)

Distr

Distribute -7

a^2 + 7 a - 7 a - 49

SubTerm

Subtract term

a^2 - 49

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 37 Page 61

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