Problem of the Week

Updated at Sep 11, 2017 10:05 AM

This week's problem comes from the algebra category.

How can we compute the factors of \({(2x)}^{2}-4\)?

Let's begin!



\[{(2x)}^{2}-4\]

1
Rewrite it in the form \({a}^{2}-{b}^{2}\), where \(a=2x\) and \(b=2\).
\[{(2x)}^{2}-{2}^{2}\]

2
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[(2x+2)(2x-2)\]

3
Factor out the common term \(2\).
\[2(x+1)(2x-2)\]

4
Factor out the common term \(2\).
\[2(x+1)\times 2(x-1)\]

5
Simplify.
\[4(x+1)(x-1)\]

Done
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