1
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simply 3x squared minus 8x plus 7 plus 2x to the third minus x squared plus eight x minus 3

2
00:00:11,000 --> 00:00:14,800
so when we simplify this we're essentially going to add up like terms

3
00:00:14,800 --> 00:00:19,133
and just as a reminder we can only add or subtract like terms or simplify like terms

4
00:00:19,133 --> 00:00:24,533
and just a reminder and what I mean by that if I had an x squared to an x squared

5
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these are like terms they're both x terms raised to the same power

6
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the same degree

7
00:00:30,067 --> 00:00:35,800
so if I have one x squared and another x squared well then I have 2x squared - this is 2x squared

8
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If I have an x to the third - let's say I have 3x to thirds plus another 4x to the thirds

9
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Well that means I have 7x to the thirds - 7x to the thirds

10
00:00:45,400 --> 00:00:53,333
I can't take an x squared and add it to an x to the third I cannot simplify this in any way, so this you cannot simplify

11
00:00:53,333 --> 00:00:59,333
cannot simply - these are not like terms just because they both have Xs

12
00:00:59,333 --> 00:01:03,400
The Xs are not to - they are not to the same degree

13
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With that in mind let's look at the Xs to the same degree

14
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Let's start with the highest degree

15
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So the highest degree or the highest exponent on an x here - is actually this x to the third here

16
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but it looks like the only one it's the only place where we're raising x to the third power

17
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so that can't be merged or added or subtracted to anything else

18
00:01:21,800 --> 00:01:23,467
so let's just write that down.

19
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so we have 2x to the third

20
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and let's look at the x squared terms. We have 3x squared over there

21
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and we have a minus or we can view as a negative x squared over there

22
00:01:37,133 --> 00:01:43,000
so if we want to simplify we can add these two terms - we can add- so let me just write it down

23
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we can add 3x squared to negative x squared

24
00:01:47,800 --> 00:01:50,933
so I'm just rearranging it really right now

25
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I'm putting the like terms next to each other so it'll be easy to simplify

26
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now let's just worry about the x to the first terms or just the x terms

27
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you have a negative 8x term right over here

28
00:02:00,867 --> 00:02:03,000
so let me write it over here

29
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negative 8x and then you have a positive 8x term right over here, so let me write that down

30
00:02:09,000 --> 00:02:11,067
so positive 8x

31
00:02:11,067 --> 00:02:13,733
and then finally let's look at the constant terms

32
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you can view those as times x to the zeroth power

33
00:02:16,733 --> 00:02:21,400
and the constant terms are - you have a positive 7 over here - so plus 7

34
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and then you have a negative 3 over here

35
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you have a negative 3

36
00:02:27,067 --> 00:02:31,133
so all I'll I've done is I've really just used the communative property of addition

37
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to just change the order - or addition and subtraction - to change the order in which I'm doing this

38
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I've just rearranged the things so the like terms are next to each other

39
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but now we can simplify

40
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so we have 2x to the third - nothing to simplify that with

41
00:02:45,333 --> 00:02:50,733
but then if we subtract - if we have - let me do that in the same blue color

42
00:02:50,733 --> 00:02:55,200
if we have 3x squared and from that we're taking away an x squared

43
00:02:55,200 --> 00:02:57,733
well, we're only gonna have 2x squared left

44
00:02:57,733 --> 00:03:01,067
so that's gonna be plus 2x squared

45
00:03:01,067 --> 00:03:04,667
and then over here if we have negative 8 Xs

46
00:03:04,667 --> 00:03:08,400
and then we add 8 Xs to it or you can actually swap these around

47
00:03:08,400 --> 00:03:15,067
you could view it as you are subtracting 8 x from positive 8x

48
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we'll those are just going to cancel out

49
00:03:16,733 --> 00:03:22,067
so it's just going to be zero - I could just write plus zero here, but that'd just be redundant it wouldn't change the value

50
00:03:22,067 --> 00:03:27,067
and then finally I have a plus 7 minus 3 well that is just clearly

51
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7 minus 3 is 4 so I have plus 4

52
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And we're done! We've simplified it!

53
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2x to the third plus 2 x squared plus 4