>> The first thing we need to do, as always, is think about what adds to equal
4, and multiplies to equal 4 times 1, or 4? In this case, our numbers are 2 and
2. So instead of 4x, we can write 2x plus 2x, and of course the rest of the
expression as well. Then something interesting happens when we try to factor the
first two terms and the second two terms. The first two are pretty normal, we
pull out a 2x from the 4x squared plus 2x, but then when we get to 2x plus 1
Well there are no common factors that 2x and 1 have aside from 1. So that's
exactly what we write, 1. And then the last two terms, 2x plus 1. Conveniently,
this still works out perfectly and we get 2x plus 1 times 2x plus 1. Which we
can also write as 2x plus 1 the quantity squared.