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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 65 Page 71

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

(x+4)(x-4)

Practice makes perfect

Look closely at the expression x^2-16. It can be expressed as the difference of two perfect squares.

x^2-16

Write as a power

x^2-4^2

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. x^2- 4^2 ⇔ ( x+ 4)( x- 4)

Checking Our Answer

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

(x+4)(x-4)

Distribute x + 4

x (x + 4) - 4 (x + 4)

Distribute x

x^2+4x - 4(x + 4)

Distribute -4

x^2+4x-4x-16

Subtract term

x^2-16

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