1
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Factor out the greatest common factor.

2
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And the expression it gives us is 4x^4 y + 8x^3 y.

3
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When they say to factor out the greatest common factor,

4
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they're essentially telling us to find the greatest common factor of

5
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4x^4 y and 8x^3 y and factor it out of this expression, kind of undistribute it.

6
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And to find that greatest common factor, now I always put it in quotes when we speak in kind of algebraic terms.

7
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Because we don't really know what "x" and "y" are - whether they're positive or negative,

8
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or whether they are greater than or less than 1.

9
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So it's not always going to be the greatest absolute number,

10
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but it's kind of the greatest and it contains the most terms of these two expressions, these two monomials.

11
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So if we were to essentially factor out 4x^4 y, it would look like this.

12
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We do the prime factorization of 4, which is just 2 times 2, times x^4, which is "x" times "x" times "x" times "x",

13
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times "y", and we just kind of expanded it out as the product of its basic constituents.

14
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Now let's do the same thing for 8x^3, so we have in this situation 8x^3 y.

15
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So the prime factorization of 8 is 2 times 2 times 2.

16
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It's 2 times 2 times 2.

17
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Prime, or I should say, the factorization of x^3, the expansion of it,

18
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is just "x" times "x" times "x", x multiplied by itself 3 times.

19
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And then we are multiplying everything by "y" here.

20
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So what factors are common to both of these? And you want to I include as many as possible to find

21
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this "greatest common factor".

22
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So we have 2 2's here, 3 2's here,

23
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so we only have 2 2's in common in both of them.

24
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We have 4 "x"s here, only 3 "x"s here, so we only have three "x"s in common.

25
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3 "x"s and 3 "x"s.

26
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We have a "y" here and a "y" here, so "y" is common to both, to both expressions,

27
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So the greatest common factor here is going to be 2 times 2 times "x" times "x" times "x"

28
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times "y", or 4x^3, 4x^3 y.

29
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So this is what we want to factor out.

30
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So that means that we can write this as