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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 53 Page 70

Use the difference of squares to factor the expression.

Adriano's answer is correct.
Explanation: See solution.

Practice makes perfect

Let's factor the expression to check if either answer is correct. We can begin by factoring out any common factors using the Distributive Property. x^8-x^4 ⇒ x^4(x^4-1)

Since, we only have two terms within the parentheses, we can check for a difference of squares. x^4( x^4-1) ⇕ x^4( x^2+1)( x^2-1) Then, because the first term of each factor in parentheses can still be squared, we will check for a difference of squares again. x^4(x^2+1)( x^2-1) ⇕ x^4(x^2+1)( x-1)( x+1) We cannot factor out any other terms. Therefore, Adriano correctly factored the expression.

Subchapter links

Exercises p.68-71