# 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.$4(x+1)(x-1)$Done4*(x+1)*(x-1)