1 00:00:00,571 --> 00:00:01,605 I've gotten feedback 2 00:00:01,605 --> 00:00:03,769 that all the Chuck Noris imagery in the last video 3 00:00:03,769 --> 00:00:05,703 might have been a little bit too overwhelming. 4 00:00:05,703 --> 00:00:07,105 So, for this video, I've included 5 00:00:07,105 --> 00:00:09,769 something a little bit more soothing. 6 00:00:09,769 --> 00:00:11,770 So let's try to simplify some more expressions. 7 00:00:11,770 --> 00:00:13,370 and we'll see we're just applying ideas 8 00:00:13,370 --> 00:00:15,272 that we already knew about. 9 00:00:15,272 --> 00:00:20,998 So, let's say I want to simplify the expression 2(3x + 5). 10 00:00:21,059 --> 00:00:23,703 Well, this literally means two "3x + 5". 11 00:00:23,703 --> 00:00:25,855 So, this is the exact same thing as... 12 00:00:25,855 --> 00:00:28,032 So this is one "3x + 5", 13 00:00:28,032 --> 00:00:30,639 and then to that, I'm going to add another "3x + 5". 14 00:00:30,639 --> 00:00:33,904 This is literally what 2(3x + 5) means. 15 00:00:33,904 --> 00:00:36,104 Well this, is the same thing as... 16 00:00:36,104 --> 00:00:37,688 if we're gonna just have a look right over here, 17 00:00:37,688 --> 00:00:40,005 we have now two "3x". 18 00:00:40,005 --> 00:00:49,014 So, we can write it as 2(3x), plus we have two "5". 19 00:00:49,087 --> 00:00:52,171 So, plus 2(5). 20 00:00:52,171 --> 00:00:53,188 But, you might say: "Hey Sal, 21 00:00:53,188 --> 00:00:55,704 isn't this just the distributive property 22 00:00:55,704 --> 00:00:57,037 that I know from arithmetic? 23 00:00:57,037 --> 00:01:05,324 I've essentially just distributed the two "2(3x)" plus "2(5)", 24 00:01:05,324 --> 00:01:08,434 And I would tell you: "Yes, it is!" 25 00:01:08,434 --> 00:01:09,854 And, the whole reason why I'm doing this, 26 00:01:09,854 --> 00:01:10,780 is just to show you that it is 27 00:01:10,796 --> 00:01:12,769 exactly what you all already know. 28 00:01:12,769 --> 00:01:14,355 But with that out of the way, 29 00:01:14,355 --> 00:01:15,704 let's continue to simplify it. 30 00:01:15,704 --> 00:01:21,270 So, when you multiply the 2(3x), you get 6x. 31 00:01:21,270 --> 00:01:24,703 If you multiply the 2(5), you get 10. 32 00:01:24,703 --> 00:01:28,482 So, this simplifies to 6x + 10. 33 00:01:28,482 --> 00:01:30,317 Now, let's try something that's a little bit more evolved. 34 00:01:30,396 --> 00:01:34,230 Once again, really just things that you already know. 35 00:01:34,230 --> 00:01:54,591 So, let's say I had 7(3y - 5) - 2(10 +4y). 36 00:01:54,591 --> 00:01:56,503 Let's see if we can simplify this. 37 00:01:56,503 --> 00:01:59,638 Well, let's work on the left-hand side of the expression. 38 00:01:59,638 --> 00:02:01,571 The 7(3y - 5). 39 00:02:01,571 --> 00:02:03,438 We just have to distribute the "7". 40 00:02:03,438 --> 00:02:06,038 So, this is gonna be 7 times 3y, 41 00:02:06,038 --> 00:02:08,188 which is going to give us 21y, 42 00:02:08,188 --> 00:02:11,761 Or, if I had three "y" seven times, this is going to be 21y 43 00:02:11,771 --> 00:02:13,190 (either way you want to think about it). 44 00:02:13,190 --> 00:02:15,187 And then I have "7" times... 45 00:02:15,187 --> 00:02:16,271 We're going to be careful with the sign. 46 00:02:16,271 --> 00:02:18,370 This is "7" times negative 5. 47 00:02:18,370 --> 00:02:22,521 "7" times "-5" is "-35". 48 00:02:22,521 --> 00:02:24,038 So, we simplified this part of it. 49 00:02:24,038 --> 00:02:25,271 Let's simplify the right hand side. 50 00:02:25,271 --> 00:02:27,605 So, you might be tempted to say: 51 00:02:27,605 --> 00:02:29,701 "Oh, "2" times "10" and "2" times "4y", 52 00:02:29,701 --> 00:02:31,472 and then subtract them, 53 00:02:31,472 --> 00:02:33,996 and if you do that right and distribute the subtraction, 54 00:02:33,996 --> 00:02:35,035 it would work out. 55 00:02:35,035 --> 00:02:39,478 But, I like to think of this as... "-2". 56 00:02:39,478 --> 00:02:42,103 And we're just going to distribute the "-2" times "10", 57 00:02:42,103 --> 00:02:46,938 and then we're going to distribute the "-2" times "4y". 58 00:02:46,938 --> 00:02:53,303 So, "-2" times "10" is "-20". 59 00:02:53,303 --> 00:02:56,303 (minus 20, right over here). 60 00:02:56,303 --> 00:02:58,945 And then "-2" times "4y"... 61 00:02:58,945 --> 00:03:00,493 "-2" times "4" is "-8", 62 00:03:00,493 --> 00:03:03,299 so it's going to be "-8y". 63 00:03:03,299 --> 00:03:06,438 So, let's write a "-8y" right over here. 64 00:03:06,438 --> 00:03:08,521 And now we're done simplifying. 65 00:03:08,521 --> 00:03:10,770 Well no, there's a little bit more that we can do. 66 00:03:10,770 --> 00:03:13,570 We can't add the "21y" to the "-35" or the "-20", 67 00:03:13,570 --> 00:03:16,355 because these are adding different things 68 00:03:16,355 --> 00:03:17,605 or subtracting different things. 69 00:03:17,605 --> 00:03:20,606 But we do have two things that are multiplying "y". 70 00:03:20,606 --> 00:03:22,303 We have the... 71 00:03:22,303 --> 00:03:24,571 Let me do them all in this green color. 72 00:03:24,571 --> 00:03:26,105 You have 21y, right over here. 73 00:03:26,105 --> 00:03:33,170 And then, from that we are subtracting 8y. 74 00:03:33,170 --> 00:03:34,903 So 21 of something... 75 00:03:34,903 --> 00:03:37,520 If I have 21 of something and I take 8 of them away, 76 00:03:37,520 --> 00:03:39,188 I'm left with 13 of that something. 77 00:03:39,188 --> 00:03:42,438 So, those are going to simplify to 13y. 78 00:03:42,438 --> 00:03:51,715 And then, I have "-35" minus "20". 79 00:03:51,715 --> 00:03:56,216 And so, that's just going to simplify to "-55". 80 00:03:56,216 --> 00:03:57,837 So, this whole thing simplified, 81 00:03:57,837 --> 00:03:59,769 using a little bit of distributive property 82 00:03:59,769 --> 00:04:01,938 and combining similar or like terms, 83 00:04:01,938 --> 00:04:06,400 we got to "13y - 55".