1
00:00:00,000 --> 00:00:00,600


2
00:00:00,600 --> 00:00:04,012
We're asked to simplify this huge, long expression here. x

3
00:00:04,012 --> 00:00:07,719
to the third plus 3x minus 6-- that's in parentheses-- plus

4
00:00:07,719 --> 00:00:10,699
negative 2x squared plus x minus 2.

5
00:00:10,699 --> 00:00:13,419
And then minus the quantity 3x minus 4.

6
00:00:13,419 --> 00:00:15,789
So a good place to start, we'll just rewrite this and

7
00:00:15,789 --> 00:00:18,549
see if we can eliminate the parentheses in this step.

8
00:00:18,550 --> 00:00:20,420
So let's just start at the beginning.

9
00:00:20,420 --> 00:00:24,270
We have the x to the third right over there.

10
00:00:24,269 --> 00:00:28,434
So x to the third and then plus 3x-- I'll do that in

11
00:00:28,434 --> 00:00:29,684
pink-- plus 3x.

12
00:00:29,684 --> 00:00:32,089


13
00:00:32,090 --> 00:00:36,510
And then we have a minus 6.

14
00:00:36,509 --> 00:00:38,570
And we don't have to put the parentheses around there,

15
00:00:38,570 --> 00:00:40,770
those don't really change anything.

16
00:00:40,770 --> 00:00:42,750
And we don't have to even write these-- do anything with

17
00:00:42,750 --> 00:00:43,479
these parentheses.

18
00:00:43,479 --> 00:00:44,224
We can eliminate them.

19
00:00:44,225 --> 00:00:45,759
Just because there's a positive sign out here we

20
00:00:45,759 --> 00:00:47,129
don't have to distribute anything.

21
00:00:47,130 --> 00:00:48,670
Distributing a positive sign doesn't do

22
00:00:48,670 --> 00:00:49,980
anything to these numbers.

23
00:00:49,979 --> 00:00:53,489
So then plus, we have a negative 2x squared.

24
00:00:53,490 --> 00:00:56,600
So this term right here is negative 2x

25
00:00:56,600 --> 00:00:58,440
squared, or minus x squared.

26
00:00:58,439 --> 00:01:00,589
And then we have a plus x.

27
00:01:00,590 --> 00:01:01,890
We have a plus x.

28
00:01:01,890 --> 00:01:04,939


29
00:01:04,939 --> 00:01:06,435
Then we have a minus 2.

30
00:01:06,435 --> 00:01:09,340


31
00:01:09,340 --> 00:01:12,180
Then we have a negative sign times this whole expression.

32
00:01:12,180 --> 00:01:13,730
So we're going to have to distribute the negative sign.

33
00:01:13,730 --> 00:01:16,189
So it's a positive 3x, but it's being multiplied by

34
00:01:16,189 --> 00:01:17,250
negative 1.

35
00:01:17,250 --> 00:01:19,480
So it's really a negative 3x.

36
00:01:19,480 --> 00:01:25,040
So minus 3x, then you have a negative-- you can imagine

37
00:01:25,040 --> 00:01:27,240
this is a negative 1 implicitly out here-- negative

38
00:01:27,239 --> 00:01:28,089
1 times negative 4.

39
00:01:28,090 --> 00:01:29,570
That's a positive 4.

40
00:01:29,569 --> 00:01:30,819
So plus 4.

41
00:01:30,819 --> 00:01:33,409


42
00:01:33,409 --> 00:01:36,019
Now, we could combine terms of similar

43
00:01:36,019 --> 00:01:37,259
degree, of the same degree.

44
00:01:37,260 --> 00:01:39,359
Now, first we have an x to the third term and I think it's

45
00:01:39,359 --> 00:01:42,150
the only third degree term here, because we have x being

46
00:01:42,150 --> 00:01:43,760
raised to the third power.

47
00:01:43,760 --> 00:01:44,770
So let me just rewrite it here.

48
00:01:44,769 --> 00:01:45,834
We have x to the third.

49
00:01:45,834 --> 00:01:48,399
And now let's look at our x squared terms. Looks like we

50
00:01:48,400 --> 00:01:49,680
only have one.

51
00:01:49,680 --> 00:01:51,340
We only have this term right here.

52
00:01:51,340 --> 00:01:54,740
So we have minus 2x squared.

53
00:01:54,739 --> 00:01:56,129
And then what about our x terms?

54
00:01:56,129 --> 00:02:00,979
We have a 3x plus an x minus a 3x again.

55
00:02:00,980 --> 00:02:04,143
So that 3x minus the 3x would cancel out, and you're just

56
00:02:04,143 --> 00:02:05,489
left with an x.

57
00:02:05,489 --> 00:02:07,489
So plus x.

58
00:02:07,489 --> 00:02:10,620
And then finally our constant terms. Negative 6

59
00:02:10,620 --> 00:02:12,810
minus 2 plus 4.

60
00:02:12,810 --> 00:02:15,789
Negative 6 minus 2 gets us to negative 8.

61
00:02:15,789 --> 00:02:20,150
Plus 4 is negative 4.

62
00:02:20,150 --> 00:02:20,849
And we are done.

63
00:02:20,849 --> 00:02:22,560
We have simplified the expression.

64
00:02:22,560 --> 00:02:24,569
Now we just have a four term polynomial.

65
00:02:24,569 --> 00:02:26,332