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McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

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Exercise 19 Page 61

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

(r+3t)(r-3t)

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Look closely at the expression r^2-9t^2. It can be expressed as the difference of two perfect squares.

r^2-9t^2

WritePow

Write as a power

r^2-3^2t^2

ProdPowII

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

r^2-(3t)^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. r^2-( 3t)^2 ⇔ ( r+ 3t)( r- 3t)

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

(r + 3t) (r - 3t)

Distr

Distribute r + 3t

r(r + 3t) - 3t(r + 3t)

Distr

Distribute r

r^2 + 3 rt - 3t(r + 3t)

Distr

Distribute -3t

r^2 + 3 rt - 3 rt - 9t^2

SubTerm

Subtract term

r^2 - 9t^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 19 Page 61

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