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Chapter 0: Problem 112

Factor completely. $$(x+y)^{4}-100(x+y)^{2}$$

Short Answer

Expert verified
\((x+y)^{4}-100(x+y)^{2} = (11(x+y)^{2})(-(9)(x+y)^{2})\)

Step by step solution

01

Identify the Quadratic Form

The given expression is of the form \(a^{2}-b^{2}\), which can be written as \((a+b)(a-b)\), where \(a=(x+y)^{2}\) and \(b=10\). Thus \(a^{2}\) is \((x+y)^{4}\) and \(b^{2}\) is \(100(x+y)^{2}\).
02

Apply the Difference of Squares Formula

Use the formula for the difference of squares to rewrite the expression: \((x+y)^{4}-100(x+y)^{2} = ((x+y)^{2}+10(x+y)^{2})((x+y)^{2}-10(x+y)^{2})\)
03

Final Expression

Simplify the resulting expression to get the final answer: \((x+y)^{4}-100(x+y)^{2} = (11(x+y)^{2})(-(9)(x+y)^{2})\)

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Most popular questions from this chapter

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

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Perform the indicated operations. Simplify the result, if possible. $$\left(2-\frac{6}{x+1}\right)\left(1+\frac{3}{x-2}\right)$$
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