1 00:00:00,716 --> 00:00:06,521 Let's say that I've got two Chuck Norrises (or maybe it's Chuck Norri) 2 00:00:06,521 --> 00:00:13,205 and to that I am going to add another three Chuck Norrises 3 00:00:13,205 --> 00:00:15,302 So I'm going to add another three Chuck Norrises 4 00:00:15,302 --> 00:00:20,204 And this might seem a little bit obvious but how many Chuck Norrises do I now have? 5 00:00:20,204 --> 00:00:26,671 Well, two Chuck Norrises - we can represent this as literally a Chuck Norris plus a Chuck Norris 6 00:00:26,671 --> 00:00:31,740 So let me do that, a Chuck Norris plus another Chuck Norris - two Chuck Norrises. 7 00:00:31,740 --> 00:00:35,786 You can also view that as 2 times Chuck Norris and this is just another way of representing it 8 00:00:35,817 --> 00:00:39,291 And three Chuck Norrises 9 00:00:39,291 --> 00:00:45,553 You could view that as a Chuck Norris, plus a Chuck Norris, plus another Chuck Norris 10 00:00:45,553 --> 00:00:50,003 And so we would have a grand total (and this might be very simple for you) 11 00:00:50,003 --> 00:00:54,538 But you would have a grand total of 1..2..3..4..5 Chuck Norrises 12 00:00:54,538 --> 00:00:57,903 So this would be equal to 13 00:00:57,903 --> 00:01:00,893 5 Chuck Norrises 14 00:01:00,893 --> 00:01:02,653 Now let's get a little bit more abstract here 15 00:01:02,653 --> 00:01:05,299 Chuck Norris is a very tangible thing 16 00:01:05,299 --> 00:01:09,153 So let's go to a little bit more of the traditional algebraic notation. 17 00:01:09,153 --> 00:01:11,955 If I have two X's 18 00:01:11,955 --> 00:01:16,371 And remember 2x - you can view this as two X's or two times X. 19 00:01:16,371 --> 00:01:21,187 And to that I were to add 3 X's 20 00:01:21,248 --> 00:01:23,309 How many X's do I have? 21 00:01:23,309 --> 00:01:27,340 Well, once again, 2 X's that's 2 times X and you can view it as an X plus an X. 22 00:01:27,340 --> 00:01:32,448 We don't know what the value of X is but whatever that value is we can add it to itself 23 00:01:32,448 --> 00:01:35,050 And then three X's are going to be that value 24 00:01:35,050 --> 00:01:37,711 I'll do it in that same green colour 25 00:01:37,711 --> 00:01:39,154 Three X's are going to be that value 26 00:01:39,169 --> 00:01:40,181 plus that value 27 00:01:40,181 --> 00:01:43,849 plus whatever that value is 28 00:01:43,849 --> 00:01:46,609 And so how many X's do I now have? 29 00:01:46,609 --> 00:01:50,812 Well, I'm going to have 1..2..3..4..5 X's 30 00:01:50,812 --> 00:01:56,413 So 2x plus 3x is equal to 31 00:01:56,413 --> 00:01:57,091 5x 32 00:01:57,122 --> 00:02:00,283 And if you think about it, all we really did (and hopefully you conceptually get it) 33 00:02:00,314 --> 00:02:04,013 We just added the two numbers that were multiplying the X. 34 00:02:04,059 --> 00:02:06,227 And these numbers, the two or the three 35 00:02:06,227 --> 00:02:07,198 they're called "coefficients" 36 00:02:07,213 --> 00:02:12,969 Very fancy word - but it's just this constant number, this regular number, that's multiplied by the variable. 37 00:02:12,969 --> 00:02:16,749 You just added the two and the three to get your 5x. 38 00:02:16,749 --> 00:02:18,826 Now let's think about this a little bit more 39 00:02:18,903 --> 00:02:23,247 Let's go back to this original expression, the two Chuck Norrises plus three Chuck Norrises. 40 00:02:23,247 --> 00:02:26,367 Let's say, to that we were to add 41 00:02:26,367 --> 00:02:28,866 Let's say we were to add some type of a... 42 00:02:28,866 --> 00:02:31,867 Let's say we were to add seven plums over here 43 00:02:31,867 --> 00:02:34,066 So this is my drawing of a plum 44 00:02:34,066 --> 00:02:38,135 So we have seven plums plus two Chuck Norrises plus three Chuck Norrises 45 00:02:38,135 --> 00:02:40,984 And let's say that I add another two plums 46 00:02:40,984 --> 00:02:43,282 I add another two plums here 47 00:02:43,282 --> 00:02:45,071 So what would this whole thing be? 48 00:02:45,071 --> 00:02:47,846 Well, I wouldn't add the seven to the two to the three plus the two 49 00:02:47,846 --> 00:02:49,971 We're adding different things here! 50 00:02:49,971 --> 00:02:51,949 You have two Chuck Norrises and three Chuck Norrises 51 00:02:51,949 --> 00:02:54,718 So they're still going to simplify to five Chuck Norrises 52 00:02:54,718 --> 00:02:57,065 And then we would separately think about the plums 53 00:02:57,065 --> 00:02:59,302 We have seven plums and we're adding another two plums 54 00:02:59,302 --> 00:03:01,497 We're going to have nine plums 55 00:03:01,497 --> 00:03:04,486 Plus nine plums 56 00:03:04,486 --> 00:03:07,565 So this simplifies to five Chuck Norrises and nine plums 57 00:03:07,565 --> 00:03:12,053 Similarly, over here, if I had instead of just 2x plus 3x 58 00:03:12,053 --> 00:03:15,368 If I had 7y 59 00:03:15,368 --> 00:03:20,215 7y plus 2x plus 3x plus 2y 60 00:03:20,215 --> 00:03:22,080 What do I now have? 61 00:03:22,080 --> 00:03:23,868 Well, I can't add the X's and the Y's 62 00:03:23,868 --> 00:03:26,430 They could very well represent a different number 63 00:03:26,430 --> 00:03:30,119 So all I can do is really, add the X's (and then I get the 5x) 64 00:03:30,134 --> 00:03:31,705 And then I'd separately add the Y's 65 00:03:31,705 --> 00:03:34,556 If have seven Y's and to that I add two Y's 66 00:03:34,556 --> 00:03:36,724 I'm going to have nine Y's 67 00:03:36,724 --> 00:03:40,138 If I have seven of something and I have two of something, I now have nine of that something 68 00:03:40,138 --> 00:03:43,176 So I'm going to have nine Y's 69 00:03:43,176 --> 00:03:45,225 So you add that (we'll do that in a different colour) 70 00:03:45,225 --> 00:03:47,476 You add this 71 00:03:47,476 --> 00:03:48,710 ... and this 72 00:03:48,710 --> 00:03:50,324 ... you get that 73 00:03:50,324 --> 00:03:53,908 You add the X's 74 00:03:53,908 --> 00:03:56,490 ... you get that right over there 75 00:03:56,490 --> 00:03:57,762 So hopefully that makes a little sense 76 00:03:57,762 --> 00:03:59,207 Actually, I'll throw out one more idea 77 00:03:59,207 --> 00:04:01,077 So given this, what would happen if I were to have 78 00:04:01,077 --> 00:04:08,681 2x plus 1 plus 7x plus 5? 79 00:04:08,681 --> 00:04:10,977 Well, once again, you might be tempted to add the two plus the one 80 00:04:10,977 --> 00:04:12,323 But they're adding different things! 81 00:04:12,323 --> 00:04:14,490 These are two X's, this is just the number one 82 00:04:14,490 --> 00:04:17,623 So you really just have to add the X's together. 83 00:04:17,623 --> 00:04:19,184 So you're going to say "well I've got two X's 84 00:04:19,184 --> 00:04:21,694 and I'm going to add seven X's to that" 85 00:04:21,694 --> 00:04:23,605 Well that means that I now have nine X's 86 00:04:23,605 --> 00:04:24,997 And then separately, you would say 87 00:04:24,997 --> 00:04:27,128 "Well, I've got just the abstract number one 88 00:04:27,128 --> 00:04:28,597 and then I've got another five" 89 00:04:28,597 --> 00:04:32,597 One plus five is going to be equal to six.