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Pearson Algebra 2 Common Core, 2011 View details

3. Rational Functions and Their Graphs

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Exercise 74 Page 523

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

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

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Look closely at the expression 4x^2-9. It can be expressed as the difference of two perfect squares.

4x^2-9

WritePow

Write as a power

2^2x^2-3^2

ProdPowII

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

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

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

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

Distr

Distribute 2x + 3

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

Distr

Distribute 2x

4x^2 + 6x - 3(2x + 3)

Distr

Distribute -3

4x^2 + 6x - 6x - 9

SubTerm

Subtract term

4x^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!

Subchapter links

Lesson Check p.521

Practice and Problem-Solving Exercises p.521-523

Standardized Test Prep p.523

Exercise 74 Page 523

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