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McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 67 Page 71

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

(1+10p)(1-10p)

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Look closely at the expression 1-100p^2. It can be expressed as the difference of two perfect squares.

1-100p^2

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Write as a power

1^2-10^2p^2

ProdPowII

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

1^2-(10p)^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. 1^2-( 10p)^2 ⇔ ( 1+ 10p)( 1- 10p)

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

(1+10p)(1-10p)

Distr

Distribute (1+10p)

1+10p-10p(1+10p)

Distr

Distribute -10p

1+10p-10p-100p^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.68-71

Exercise 67 Page 71

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