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McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

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Exercise 15 Page 61

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

(q+11)(q-11)

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Look closely at the expression q^2-121. It can be expressed as the difference of two perfect squares.

q^2-121

WritePow

Write as a power

q^2-11^2

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. q^2- 11^2 ⇔ ( q+ 11)( q- 11)

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

(q + 11) (q - 11)

Distr

Distribute (q+11)

q (q + 11) - 11 (q + 11)

Distr

Distribute q

q^2 + 11q - 11(q + 11)

Distr

Distribute -11

q^2 + 11q - 11q - 121

SubTerm

Subtract term

q^2 - 121

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 15 Page 61

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