1
00:00:01,259 --> 00:00:06,443
Multiply (5a - 2)(4a^2 + 3a - 1)

2
00:00:06,443 --> 00:00:09,659
So here we are multiplying a binomial by a trinomial

3
00:00:09,659 --> 00:00:12,591
So the FOIL tool will not work here

4
00:00:12,591 --> 00:00:16,509
It would only work if you were multiplying a binomial by another binomial

5
00:00:16,509 --> 00:00:20,292
So here we really have to rely on the distributive property. What we can do is

6
00:00:20,292 --> 00:00:26,592
we can distribute this entire trinomial onto the binomial. We we can multiply 4a^2

7
00:00:26,592 --> 00:00:35,926
plus 3a -1 times 5a and then multiply (4a^2 + 3a -1) times -2.

8
00:00:35,926 --> 00:00:47,592
So that would give us, let me do it this way. That would give us 5a times 4a^2 +3a -1

9
00:00:47,592 --> 00:01:05,328
and then we would have a plus -2 times 4a^2 plus 3a -1. I've just distributed this

10
00:01:05,328 --> 00:01:11,425
onto each term over here you see the 5a -2 each term is now being multiplied by this entire thing.

11
00:01:11,425 --> 00:01:17,644
And now we can distribute the 5a onto this term. So we have 5a times 4a^2.

12
00:01:17,644 --> 00:01:26,194
So we can multiply the 5 times the 4 we get 20. a times the a^2 is a^3. Then we do

13
00:01:26,194 --> 00:01:33,794
5a times 3a. 5 times 3 is fifteen. a times a is a^2.

14
00:01:33,794 --> 00:01:42,042
Then we have 5a times -1, well thats just going to be -5a. Now we do this part,

15
00:01:42,042 --> 00:01:51,542
Plus -2 times 4a^2. -2 times four is -8a^2. So we just did that...

16
00:01:51,542 --> 00:02:03,978
-2 times 3a is -6a. And then finally you have -2 times -1. Well a negative times a negative is a positive.

17
00:02:03,978 --> 00:02:08,744
So that is postive 2 and now we can combine like terms.

18
00:02:08,744 --> 00:02:15,060
We only have one ^3 term over here. We only have the 20a^3. So lets just write that down.

19
00:02:15,060 --> 00:02:23,195
And then lets look at our a^2 terms we have a 15a^2 right over here and we have another

20
00:02:23,195 --> 00:02:31,960
-8a^2. So if I have 15 of something and I subtract 8 from that then I have 7 of that something left.

21
00:02:31,960 --> 00:02:44,945
So 15 minus 8 is 7. And then we have a -5a. And to that we're going to add -6a.

22
00:02:44,945 --> 00:02:48,944
So we are already -5 and to that we're going to be another -6.

23
00:02:48,944 --> 00:02:56,043
We going to be 6 more negative. So that is -11a. And then finally we have this constant out here.

24
00:02:56,043 --> 00:02:59,678
We have this plus 2. No I'll show you another way to get this exact same answer.

25
00:02:59,678 --> 00:03:03,661
We are done. We have simplified, and we have combined all our like terms.

26
00:03:03,661 --> 00:03:07,210
Another way to do this is just like doing the distributive property twice. But it's essentially

27
00:03:07,210 --> 00:03:13,327
more analogous to how we multiply numbers. So if we do it like this we could take this

28
00:03:13,327 --> 00:03:23,993
expression up here. We could take 4a^2 plus 3a -1. And then multiply it by this second expression.

29
00:03:23,993 --> 00:03:29,361
So times.... and I'll write it in the same places.. and when I say places. I'm not saying

30
00:03:29,361 --> 00:03:34,211
powers of ten, I'm saying powers of a. So this is in the first a power of a space.

31
00:03:34,211 --> 00:03:39,794
So 5a, see we have first powers of a in this space. Minus 2 this is the zeroth power of a.

32
00:03:39,794 --> 00:03:46,761
This a to zeroth place instead of the ones place. This is the a to the first power

33
00:03:46,761 --> 00:03:51,580
instead of the tens place. And this is a to the square power instead of the hundreds place.

34
00:03:51,580 --> 00:03:54,894
Completely analogous to what you do when you learn to multiply numbers in the first

35
00:03:54,894 --> 00:04:01,560
or second grade. So let's multiply these. First we'll multiply -2 by this entire thing.

36
00:04:01,560 --> 00:04:05,728
Remember we're just essentially doing the distributive property. When I multiply -2 by this entire thing

37
00:04:05,728 --> 00:04:15,011
I'm doing this step right over here. So -2 times -1 is positive 2. And once again theres no a there.

38
00:04:15,011 --> 00:04:19,561
So I'm going to write this in the a^0 place or the ones place.

39
00:04:19,561 --> 00:04:27,578
So it's going to be positive 2. -2 times 3a. Well that is -6a. And it's going to be in the a place.

40
00:04:27,578 --> 00:04:35,725
-6a, a to the first power place. And then -2 times 4a^2, well that's just going to be -8a^2.

41
00:04:35,725 --> 00:04:45,580
So this is-2 being multiplied by all of that gives me this. And then when I take my 5a and I multiply

42
00:04:45,580 --> 00:04:54,480
it by -1 that going to be -5a. That's going to the a place, that goes under a like term.

43
00:04:54,480 --> 00:05:01,813
then 5a times 3a, 5 times 3 is 15 and a times a is a^2. So it goes under the other a^2.

44
00:05:01,813 --> 00:05:10,780
So it's 15a^2 and then finally 5a times 4a^2 . 5 times 4 is 20. a times a^2 is a^3. So you have 20a^3.

45
00:05:10,780 --> 00:05:26,813
And now you can just add it all up. And we get 2 plus nothing is 2. -6a -5a well that's just -11a

46
00:05:26,813 --> 00:05:33,197
We still have this plus 2 here. -8a^2 plus 15a^2 well thats going to be 7a^2.

47
00:05:33,197 --> 00:05:41,248
So plus 7a^2. And then you're adding this to nothing so you have 20a^3. And we got the exact same answer.

48
00:05:41,248 --> 99:59:59,999
Cause we really did the same exact thing we just wrote it in a different way.