1 00:00:01,138 --> 00:00:08,057 Some people use the letters FOIL as a strategy for making sure they have multiplied all the terms. 2 00:00:08,057 --> 00:00:12,857 Use the FOIL approach to multiply (3x + 2)(5x - 7). 3 00:00:12,857 --> 00:00:17,133 I'm actually not one of those people who like to use the FOIL letters, 4 00:00:17,133 --> 00:00:20,380 because it's just a form of memorization as opposed to realizing 5 00:00:20,380 --> 00:00:22,860 that you're just using the distributive property, twice. 6 00:00:22,860 --> 00:00:24,718 but with that said, let's actually use FOIL, 7 00:00:24,718 --> 00:00:27,144 so that you'll see that it actually is the same thing 8 00:00:27,144 --> 00:00:29,575 as using the distributive property twice. 9 00:00:29,575 --> 00:00:32,073 So just to remember FOIL, 10 00:00:32,078 --> 00:00:34,144 it literally stands for: 11 00:00:34,144 --> 00:00:36,789 so F.O.I.L. 12 00:00:36,789 --> 00:00:41,018 The F in FOIL stands for First 13 00:00:41,018 --> 00:00:44,747 The O stands for Outside 14 00:00:44,747 --> 00:00:47,937 The I stands for Inside 15 00:00:47,937 --> 00:00:50,175 and the L stands for Last. 16 00:00:50,175 --> 00:00:51,702 So not only do you have to remember FOIL, 17 00:00:51,702 --> 00:00:54,514 but you have to remember what each of these 18 00:00:54,514 --> 00:00:56,082 letters actually stand for. 19 00:00:56,082 --> 00:00:58,172 But let's see how that applies to this 20 00:00:58,172 --> 00:01:00,004 to multiplying these two binomials. 21 00:01:00,004 --> 00:01:11,634 So we have (3x + 2)(5x - 7) 22 00:01:11,634 --> 00:01:13,867 So we're starting with the first, 23 00:01:13,867 --> 00:01:15,444 we're starting with the F 24 00:01:15,444 --> 00:01:17,219 we have to multiply the first terms 25 00:01:17,219 --> 00:01:18,722 in each of the binomials 26 00:01:18,722 --> 00:01:22,933 So that's going to be 3x*5x 27 00:01:22,933 --> 00:01:25,635 Then we do that outside terms, 28 00:01:28,220 --> 00:01:32,276 so that's going to be the 3x times the -7 29 00:01:32,276 --> 00:01:38,917 so this is going to be plus 3x times -7 30 00:01:38,917 --> 00:01:44,583 then we want to do the inside terms 31 00:01:44,583 --> 00:01:47,200 we want to do the things in green. 32 00:01:47,200 --> 00:01:49,415 so that's the 2 and the 5x 33 00:01:49,415 --> 00:01:52,067 so that's plus 2*5x 34 00:01:52,067 --> 00:01:54,939 and then we want to do the last terms 35 00:01:54,939 --> 00:01:57,118 which are 2 and -7 36 00:01:57,118 --> 00:02:00,942 so plus 2 times -7 37 00:02:00,942 --> 00:02:03,013 and we end up getting 38 00:02:03,013 --> 00:02:06,944 3x * 5x is 15x^2 39 00:02:06,944 --> 00:02:09,177 plus, or I should say minus 40 00:02:09,177 --> 00:02:10,970 because there's going to be a negative sign here 41 00:02:10,970 --> 00:02:16,287 so 3x * (-7) is -21x 42 00:02:16,287 --> 00:02:23,667 then we have 2 * 5x is 43 00:02:23,667 --> 00:02:25,491 plus 10x 44 00:02:25,491 --> 00:02:29,684 and then 2 * (-7) is -14 45 00:02:29,684 --> 00:02:31,313 now it's minus 14 46 00:02:31,313 --> 00:02:36,667 and we can these two middle terms together 47 00:02:36,667 --> 00:02:39,916 if we have -21x and we add 10x to that 48 00:02:39,916 --> 00:02:45,878 that gives us -11x 49 00:02:45,878 --> 00:02:48,077 and then these other terms over here 50 00:02:48,077 --> 00:02:53,370 we have 15x^2-11x-14 51 00:02:53,370 --> 00:02:55,056 so we just used FOIL 52 00:02:55,056 --> 00:02:57,050 what I want to do is show you that this 53 00:02:57,050 --> 00:02:59,938 is the same as using the distributive property twice 54 00:02:59,938 --> 00:03:03,685 so if we have, I'll rewrite the problem 55 00:03:03,685 --> 00:03:12,287 (3x + 2)(5x - 7) 56 00:03:12,302 --> 00:03:14,606 what we can do is distribute the (5x - 7) 57 00:03:14,606 --> 00:03:17,114 we can multiply that by the 3x 58 00:03:17,114 --> 00:03:18,603 and we can also multiply that - 59 00:03:18,603 --> 00:03:20,430 let me make it clear when I say 'that' 60 00:03:20,430 --> 00:03:21,917 I mean this whole (5x - 7) - 61 00:03:21,917 --> 00:03:25,938 we can multiply it by the 3x and also by the 2 62 00:03:25,938 --> 00:03:51,600 we get 3x (5x - 7) + 2 (5x - 7) 63 00:03:51,600 --> 00:04:00,446 and then this gives us 3x * 5x is going to be 15x^2 64 00:04:00,446 --> 00:04:07,874 3x * -7 is going to be -21x 65 00:04:07,874 --> 00:04:10,520 then, remember this step we're just applying 66 00:04:10,520 --> 00:04:11,930 the distributive property again, 67 00:04:11,930 --> 00:04:17,673 so then we have 2 * 5x is just going to be 10x 68 00:04:17,673 --> 00:04:21,718 and then we have 2 * -7 is -14 69 00:04:21,718 --> 00:04:23,941 so we actually got exactly the same result 70 00:04:23,941 --> 00:04:26,263 that we did when we applied FOIL 71 00:04:26,263 --> 00:04:31,511 and when you simplify it, you get this answer again.