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{(2x)}^{2}-4?

Let's begin!



(2x)2−4{(2x)}^{2}-4

1
Rewrite it in the form a2−b2{a}^{2}-{b}^{2}, where a=2xa=2x and b=2b=2.
(2x)2−22{(2x)}^{2}-{2}^{2}

2
Use Difference of Squares: a2−b2=(a+b)(a−b){a}^{2}-{b}^{2}=(a+b)(a-b).
(2x+2)(2x−2)(2x+2)(2x-2)

3
Factor out the common term 22.
2(x+1)(2x−2)2(x+1)(2x-2)

4
Factor out the common term 22.
2(x+1)×2(x−1)2(x+1)\times 2(x-1)

5
Simplify.
4(x+1)(x−1)4(x+1)(x-1)

Done
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