1
00:00:00,702 --> 00:00:03,188
So let's get some practice at simplifying polynomials,

2
00:00:03,368 --> 00:00:06,712
especially in the case where we have more than one variable over here

3
00:00:06,712 --> 00:00:09,281
so I have 4x squared y

4
00:00:09,281 --> 00:00:11,919
minus 3x squared minus 2 y

5
00:00:11,919 --> 00:00:13,296
so that entire expression

6
00:00:13,296 --> 00:00:14,888
plus the entire expression

7
00:00:14,888 --> 00:00:20,256
8xy minus 3x squared plus 2x squared y plus 4

8
00:00:20,256 --> 00:00:22,860
So the first thing that jumps out at me

9
00:00:22,860 --> 00:00:25,246
is that I'm just adding this expression to this expression

10
00:00:25,261 --> 00:00:27,299
so to a large degree these parentheses

11
00:00:27,299 --> 00:00:29,817
don't matter, so I can just rewrite it as

12
00:00:29,817 --> 00:00:36,001
4x squared y minus 3x squared minus 2y

13
00:00:36,001 --> 00:00:45,628
plus 8xy minus 3x squared plus 2x squared y plus 4

14
00:00:45,628 --> 00:00:49,698
Now we can try to group similar terms or like terms

15
00:00:49,698 --> 00:00:51,975
So let's think about what we have over here

16
00:00:51,975 --> 00:00:56,677
So this first term we have over here is a 4x squared y

17
00:00:56,677 --> 00:00:59,620
So can I add this to any of the other terms here?

18
00:00:59,620 --> 00:01:02,479
Do we have any other x squared y terms?

19
00:01:02,925 --> 00:01:04,686
Well, sure. This one right over here

20
00:01:04,686 --> 00:01:07,374
is another x squared y term.

21
00:01:07,374 --> 00:01:08,874
If I have 4 of something

22
00:01:08,874 --> 00:01:11,054
in this case I have 4 x squared y -s

23
00:01:11,054 --> 00:01:13,482
and I add 2 x squared y -s to it,

24
00:01:13,482 --> 00:01:16,011
how many x squared y -s do I now have?

25
00:01:16,011 --> 00:01:24,966
Well,4 plus 2: I now have 6 x squared y -s.

26
00:01:24,966 --> 00:01:27,380
Now let's move on to this term.

27
00:01:27,380 --> 00:01:30,600
So I have negative 3 x squared-s.

28
00:01:30,600 --> 00:01:33,418
Do I have any more x squared-s

29
00:01:33,418 --> 00:01:36,204
in this expression right over here?

30
00:01:36,204 --> 00:01:39,283
Well, sure, I have another negative 3 x squared

31
00:01:39,283 --> 00:01:40,690
so if I have negative 3 of something

32
00:01:40,690 --> 00:01:42,405
and then another negative 3

33
00:01:42,405 --> 00:01:45,808
I end up with negative 6 of that thing.

34
00:01:45,869 --> 00:01:49,198
So it's negative 6 x squared.

35
00:01:49,198 --> 00:01:53,622
Now let's think of this negative 2y term.

36
00:01:53,622 --> 00:01:55,831
Are there any other y -s over here?

37
00:01:55,831 --> 00:01:58,236
Well, it doesn't look like there are.

38
00:01:58,236 --> 00:02:01,561
This is xy, this is 4, there are no y -s.

39
00:02:01,561 --> 00:02:06,410
So I can't really add that to anything, so I'll just rewrite it - negative 2y.

40
00:02:06,425 --> 00:02:12,989
And then 8xy. Well, once again, doesn't seem like that can be added to anything else,

41
00:02:12,989 --> 00:02:15,042
so let's just write that over again.

42
00:02:15,042 --> 00:02:19,348
Then finally we just have the constant term plus 4.

43
00:02:19,363 --> 00:02:21,416
And it pretty much looks like we're done.

44
00:02:21,416 --> 00:02:25,416
We have simplified this as much as we can.