1 00:00:00,102 --> 00:00:02,438 We're asked to simply, or expand 2 00:00:02,438 --> 00:00:05,875 (7x + 10) ^ 2 3 00:00:05,875 --> 00:00:07,872 Now the first thing I will show you 4 00:00:07,872 --> 00:00:10,008 is exactly what you should NOT do, 5 00:00:10,008 --> 00:00:11,819 well there's this huge temptation. 6 00:00:11,819 --> 00:00:13,444 A lot of people will look at this and say 7 00:00:13,444 --> 00:00:17,438 oh, that's (7x)^2 + 10^2. 8 00:00:17,438 --> 00:00:19,900 This is WRONG. 9 00:00:19,900 --> 00:00:22,082 And I'll write it in caps. 10 00:00:22,082 --> 00:00:24,311 This is WRONG! 11 00:00:24,311 --> 00:00:25,844 What your brain is doing is thinking 12 00:00:25,844 --> 00:00:29,838 if I had 7x times 10 and I squared that, 13 00:00:29,838 --> 00:00:35,689 this would be (7x)^2 times 10^2. 14 00:00:35,689 --> 00:00:38,893 We aren't multiplying here, we're adding 7x to 10. 15 00:00:38,893 --> 00:00:41,726 So you can't just square each of these terms. 16 00:00:41,726 --> 00:00:43,398 I just wanted to highlight, 17 00:00:43,398 --> 00:00:46,788 this is completely wrong, 18 00:00:46,788 --> 00:00:49,250 and to see why it's wrong, 19 00:00:49,250 --> 00:00:50,689 you have to remind yourself 20 00:00:50,689 --> 00:00:54,637 that (7x + 10)^2 is the exact same thing 21 00:00:54,637 --> 00:01:00,767 as (7x + 10)(7x + 10). 22 00:01:00,767 --> 00:01:02,624 That's what it means to square something. 23 00:01:02,624 --> 00:01:08,058 You're multiplying it by itself twice here. 24 00:01:08,058 --> 00:01:09,451 So this is what it is, 25 00:01:09,451 --> 00:01:14,095 so we're really just multiplying 26 00:01:14,095 --> 00:01:16,278 a binomial, or two binomials, 27 00:01:16,278 --> 00:01:17,857 they just happen to be the same one, 28 00:01:17,857 --> 00:01:19,203 and you could use F.O.I.L., 29 00:01:19,203 --> 00:01:20,782 you could use the distributive method, 30 00:01:20,782 --> 00:01:22,268 but this is actually a special case: 31 00:01:22,268 --> 00:01:23,754 when you're squaring a binomial, 32 00:01:23,754 --> 00:01:25,055 so let's just think about it 33 00:01:25,055 --> 00:01:26,541 as a special case first then we can 34 00:01:26,541 --> 00:01:28,677 apply whatever we learn to this. 35 00:01:28,677 --> 00:01:30,256 So we could've just done it straight here, 36 00:01:30,256 --> 00:01:31,881 but I want to learn the general case 37 00:01:31,881 --> 00:01:33,367 so you can apply it to any problem 38 00:01:33,367 --> 00:01:34,854 that you might see. 39 00:01:34,854 --> 00:01:38,104 If I have (a+b) squared 40 00:01:38,104 --> 00:01:40,751 We already realised that it's not a squared plus b squared 41 00:01:40,751 --> 00:01:45,535 That is a plus b times a plus b. 42 00:01:45,535 --> 00:01:48,785 and now we can use the distributive property 43 00:01:48,785 --> 00:01:51,618 We can distribute this a + b times this a 44 00:01:51,618 --> 00:01:56,495 So we get, we get a times a plus b 45 00:01:56,495 --> 00:01:59,188 and we can distribute the a plus b times this b 46 00:01:59,188 --> 00:02:04,296 plus b times a plus b, and we distribute this a 47 00:02:04,296 --> 00:02:09,683 we get a squared plus ab plus b times a is another ab 48 00:02:09,683 --> 00:02:12,516 And I'm just swapping the order so it's the same as this. 49 00:02:12,516 --> 00:02:15,488 plus b times b wich is b squared. 50 00:02:15,488 --> 00:02:18,553 These are the same or these are like terms. 51 00:02:18,553 --> 00:02:21,015 So we can add them. One of something plus another of 52 00:02:21,015 --> 00:02:24,033 that something will give you two of that something. 2 ab. 53 00:02:24,033 --> 00:02:27,609 We have a squared plus 2 ab plus b squared. 54 00:02:27,609 --> 00:02:32,346 So the pattern here, the pattern here, if I have a plus b squared 55 00:02:32,346 --> 00:02:37,176 it's equal to a squared plus 2 times the product of these numbers 56 00:02:37,176 --> 00:02:42,238 plus b squared. So over here I have seven x plus ten squared 57 00:02:42,238 --> 00:02:45,674 So this is going to be equal to seven x squared 58 00:02:45,674 --> 00:02:50,690 seven x squared plus 2 times the product of seven x and 10. 59 00:02:50,690 --> 00:02:55,752 2 times seven x times 10 plus 10 squared. 60 00:02:55,752 --> 00:02:59,374 So, the difference between the rigth answer and the wrong answer 61 00:02:59,374 --> 00:03:02,718 is that you have this middle term here that you migth have 62 00:03:02,718 --> 00:03:04,854 forgot about if you did it this way. 63 00:03:04,854 --> 00:03:07,780 And this comes out when you multiplying all the different 64 00:03:07,780 --> 00:03:09,219 combinations of the terms here. 65 00:03:09,219 --> 00:03:12,563 if we simplify this, if we simplify seven x squared 66 00:03:12,563 --> 00:03:15,024 That's seven squared times x squared. 67 00:03:15,024 --> 00:03:18,136 So seven squared is 49 times x squared 68 00:03:18,136 --> 00:03:22,733 When you multiply this part out 2 times 7 times 10 69 00:03:22,733 --> 00:03:28,353 which is 140 and then we have our x. 70 00:03:28,353 --> 00:03:32,346 No other x there. And then plus 10 squared. 71 00:03:32,346 --> 99:59:59,999 So plus 100. And we are done.