# Video: Determining the Greatest Common Factor of an Algebraic Expression

Find the highest common factor of the two terms in this expression: 4π₯β΄ β 18π₯Β³.

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### Video Transcript

Find the highest common factor of the two terms in this expression, four π₯ to the fourth power minus 18π₯ cubed.

Our expression is four π₯ to the fourth power minus 18π₯ cubed. And here are the two terms. Weβre trying to find the highest common factor. The first term has a factor of four and a factor of π₯ to the fourth power. The second term has a factor of 18 and π₯ cubed. But four is not a factor of 18. But we recognize four and 18 are both even numbers, so we know they both have a factor of two. Four is two times two, and 18 is two times nine. So, both have a factor of two.

But now we need to think about how we would deal with this π₯ to the fourth power and π₯ cubed. We could say that π₯ to the fourth power is equal to π₯ to the first power times π₯ cubed. Then, we see that both of these terms have a factor of π₯ cubed. So, we can rewrite four times π₯ to the fourth power as two times π₯ cubed times two π₯. And 18π₯ cubed can be rewritten as two π₯ cubed times nine, which shows that two π₯ cubed is the highest common factor of these two terms.