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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

5. Quadratic Equations

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Exercise 64 Page 231

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

(4x+1)(4x-1)

Practice makes perfect

Look closely at the expression 16x^2 -1. It can be expressed as the difference of two perfect squares.

16x^2-1

Write as a power

4^2x^2-1^2

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

(4x)^2-1^2

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. ( 4x)^2- 1^2 ⇔ ( 4x+ 1)( 4x- 1)

Checking Our Answer

Check your answer ✓

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

(4x+1)(4x-1)

Distribute (4x-1)

4x(4x-1)+1(4x-1)

Distribute 4x

16x^2-4x+1(4x-1)

Distribute 1

16x^2-4x+4x-1

Add terms

16x^2-1

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.229

Practice and Problem-Solving Exercises p.229-231

Standardized Test Prep p.231

Mixed Review p.231