Video: Factoring by Taking Out a Binomial Factor

Factor the expression 3𝑝(𝑛³ + 1) − 𝑛³ − 1 completely.


Video Transcript

Factor the expression three 𝑝 times 𝑛 cubed plus one minus 𝑛 cubed minus one completely.

Our expression actually has four terms because three 𝑝 is a greatest common factor. So if we would redistribute, we would have three 𝑝 𝑛 cubed plus three 𝑝. And then bringing down our other terms, we would have minus 𝑛 cubed minus one. So like we said, there really are four terms, which means we could factor this by grouping.

And actually, the original expression already had began that, because we began by grouping the first two terms together and the last two terms together. And out of the first two terms, we can take out a three 𝑝. And if we did take that out, we would be left with 𝑛 cubed plus one, which again was found in our original expression.

So we needed to do the second step of taking out a greatest common factor out of the second set of parentheses. And the number that we could take out of the last two terms would be negative one. And after taking out a negative one, we will be left with 𝑛 cubed plus one. So our GCFs become one factor. And our matching parentheses become the other factor. So our final answer is three 𝑝 minus one times 𝑛 cubed plus one.

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