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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

4. Factoring Quadratic Expressions

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Exercise 61 Page 222

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

16(2t+1)(2t-1)

Practice makes perfect

To factor the given expression, we will first identify and factor out the greatest common factor. Then, we will use the formula for the difference of two squares.

Factor Out the GCF

The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 16.

64t^2-16

SplitIntoFactors

Split into factors

16* 4t^2- 16* 1

Factor out 16

16(4t^2-1)

Difference of Squares

Look closely at the expression 4t^2-1. It can be expressed as the difference of two perfect squares.

4t^2-1

Write as a power

2^2t^2-1^2

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

(2t)^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. 16 ( ( 2t)^2- 1^2 ) ⇔ 16( 2t+ 1)( 2t- 1)

Checking Our Answer

Check your answer ✓

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

16(2t+1)(2t-1)

Distribute 16

(32t+16)(2t-1)

Distribute (2t-1)

32t(2t-1)+16(2t-1)

Distribute 32t

64t^2-32t+16(2t-1)

Distribute 16

64t^2-32t+32t-16

Add terms

64t^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!

Subchapter links

Lesson Check p.221

Practice and Problem-Solving Exercises p.221-223

Standardized Test Prep p.223

Mixed Review p.223