1 00:00:00,012 --> 00:00:03,852 >> The first thing we need to do, as always, is think about what adds to equal 2 00:00:03,852 --> 00:00:07,843 4, and multiplies to equal 4 times 1, or 4? In this case, our numbers are 2 and 3 00:00:07,843 --> 00:00:11,534 2. So instead of 4x, we can write 2x plus 2x, and of course the rest of the 4 00:00:11,534 --> 00:00:15,780 expression as well. Then something interesting happens when we try to factor the 5 00:00:15,780 --> 00:00:20,021 first two terms and the second two terms. The first two are pretty normal, we 6 00:00:20,021 --> 00:00:24,255 pull out a 2x from the 4x squared plus 2x, but then when we get to 2x plus 1 7 00:00:24,255 --> 00:00:28,773 Well there are no common factors that 2x and 1 have aside from 1. So that's 8 00:00:28,773 --> 00:00:34,430 exactly what we write, 1. And then the last two terms, 2x plus 1. Conveniently, 9 00:00:34,430 --> 00:00:39,663 this still works out perfectly and we get 2x plus 1 times 2x plus 1. Which we 10 00:00:39,663 --> 00:00:43,094 can also write as 2x plus 1 the quantity squared.