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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

9. Perfect Squares

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Exercise 70 Page 71

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

(6+3c)(6-3c)

Practice makes perfect

Look closely at the expression 36-9c^2. It can be expressed as the difference of two perfect squares.

36-9c^2

Write as a power

6^2-3^2c^2

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

6^2-(3c)^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. 6^2-( 3c)^2 ⇔ ( 6+ 3c)( 6- 3c)

Checking Our Answer

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

(6+3c)(6-3c)

Distribute (6+3c)

6(6+3c)-3c(6+3c)

Distribute 6

36+18c-3c(6+3c)

Distribute -3c

36+18c-18c-9c^2

Subtract term

36-9c^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!

Subchapter links

Exercises p.68-71