﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.01,0:00:03.85,Default,,0000,0000,0000,,&gt;&gt; The first thing we need to do, as always, is think about what adds to equal Dialogue: 0,0:00:03.85,0:00:07.84,Default,,0000,0000,0000,,4, and multiplies to equal 4 times 1, or 4? In this case, our numbers are 2 and Dialogue: 0,0:00:07.84,0:00:11.53,Default,,0000,0000,0000,,2. So instead of 4x, we can write 2x plus 2x, and of course the rest of the Dialogue: 0,0:00:11.53,0:00:15.78,Default,,0000,0000,0000,,expression as well. Then something interesting happens when we try to factor the Dialogue: 0,0:00:15.78,0:00:20.02,Default,,0000,0000,0000,,first two terms and the second two terms. The first two are pretty normal, we Dialogue: 0,0:00:20.02,0:00:24.26,Default,,0000,0000,0000,,pull out a 2x from the 4x squared plus 2x, but then when we get to 2x plus 1 Dialogue: 0,0:00:24.26,0:00:28.77,Default,,0000,0000,0000,,Well there are no common factors that 2x and 1 have aside from 1. So that's Dialogue: 0,0:00:28.77,0:00:34.43,Default,,0000,0000,0000,,exactly what we write, 1. And then the last two terms, 2x plus 1. Conveniently, Dialogue: 0,0:00:34.43,0:00:39.66,Default,,0000,0000,0000,,this still works out perfectly and we get 2x plus 1 times 2x plus 1. Which we Dialogue: 0,0:00:39.66,0:00:43.09,Default,,0000,0000,0000,,can also write as 2x plus 1 the quantity squared.