﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.01,0:00:04.34,Default,,0000,0000,0000,,These would be my two factors, excellent work if you got this one correct. You Dialogue: 0,0:00:04.34,0:00:08.70,Default,,0000,0000,0000,,might have done this in a couple of ways, let's check out one of the methods. If Dialogue: 0,0:00:08.70,0:00:12.80,Default,,0000,0000,0000,,we switch the middle two terms we can see that we'll get a common factor of N in Dialogue: 0,0:00:12.80,0:00:16.93,Default,,0000,0000,0000,,the first terms and a common factor by P in the second terms. If we factor a 7 N Dialogue: 0,0:00:16.93,0:00:21.55,Default,,0000,0000,0000,,from the first two terms we'll be left with two M and positive one. And if we Dialogue: 0,0:00:21.55,0:00:26.14,Default,,0000,0000,0000,,factor a 5p from the second term, we'll be left with 1 and positive 2m. These 2 Dialogue: 0,0:00:26.14,0:00:30.83,Default,,0000,0000,0000,,factors might appear different but we just wanted to switch the order of these 2 Dialogue: 0,0:00:30.83,0:00:35.56,Default,,0000,0000,0000,,terms. Remember addition is commutative. Now that we can see there's a common Dialogue: 0,0:00:35.56,0:00:39.82,Default,,0000,0000,0000,,factor of 2m plus 1 in the first term and 2m plus 1 in the second term. We Dialogue: 0,0:00:39.82,0:00:44.70,Default,,0000,0000,0000,,factor again which leaves us with our factored form, 7n plus 5p times 2m plus 1. Dialogue: 0,0:00:44.70,0:00:49.50,Default,,0000,0000,0000,,But we could have regrouped the terms in another way. I could have grouped this Dialogue: 0,0:00:49.50,0:00:54.32,Default,,0000,0000,0000,,first term and this last term together and then kept the middle 2 terms together Dialogue: 0,0:00:54.32,0:00:58.91,Default,,0000,0000,0000,,as well. If we factor a 2m from these first 2 terms we'll be left with 7n and Dialogue: 0,0:00:58.91,0:01:04.00,Default,,0000,0000,0000,,5p. Now in this last group of terms there's only a greatest common factor of 1. Dialogue: 0,0:01:04.00,0:01:09.43,Default,,0000,0000,0000,,They don't share any variable factors or number factors. Notice that I have 7n Dialogue: 0,0:01:09.43,0:01:14.97,Default,,0000,0000,0000,,plus 5p and 7n plus 5p in these two parenthesis. This is the next common factor. Dialogue: 0,0:01:14.97,0:01:20.04,Default,,0000,0000,0000,,So, our two factors are 2m plus 1 and 7n plus 5p. Notice that these answers are Dialogue: 0,0:01:20.04,0:01:24.16,Default,,0000,0000,0000,,exactly the same. We've just switched the order of the multiplication. This Dialogue: 0,0:01:24.16,0:01:28.02,Default,,0000,0000,0000,,first parenthesis represents a number. And the second parenthesis also Dialogue: 0,0:01:28.02,0:01:31.99,Default,,0000,0000,0000,,represents a number. So, it would be like 2 times 3, would be the same as 3 Dialogue: 0,0:01:31.99,0:01:34.45,Default,,0000,0000,0000,,times 2. Our multiplication is commutative.