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McGraw Hill Integrated II, 2012 View details

8. Differences of Squares

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Exercise 1 Page 60

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

(x+3)(x-3)

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

x^2-9

WritePow

Write as a power

x^2-3^2

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- 3^2 ⇔ ( x+ 3)( x- 3)

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

(x + 3) (x - 3)

Distr

Distribute x + 3

x (x + 3) - 3 (x + 3)

Distr

Distribute x

x^2 + 3 x - 3(x + 3)

Distr

Distribute -3

x^2 + 3 x - 3 x - 9

SubTerm

Subtract term

x^2 - 9

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 1 Page 60

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