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Chapter 0: Problem 111

Factor completely. $$(x-y)^{4}-4(x-y)^{2}$$

Short Answer

Expert verified
The fully factored form of \((x-y)^{4}-4(x-y)^{2}\) is \((x-y-2)(x-y+2)(x-y)^{2}\).

Step by step solution

01

Identify a and b

First, identify a and b for the formula \((a-b)(a+b)\). Here, \(a = (x-y)^{2}\) and \(b = 2(x-y)\) are both square roots of the given equation.
02

Apply the difference-of-squares formula

Apply the formula, substituting the identified a and b into \((a-b)(a+b)\), resulting in \(((x-y)^{2} - 2(x-y))((x-y)^{2} + 2(x-y))\).
03

Simplify the result

The simplified result of the factored equation is \((x-y-2)(x-y+2)(x-y)^{2}\).

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. If the width of a rectangle is represented by \(x\) and the length is represented by \(x+200\), write a simplified algebraic expression that models the rectangle's perimeter.

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