Factor each polynomial. See Examples 5 and 6. 27-r^3

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Hello, today we're going to be factoring the following expression. So what we are given is 1331 minus M cubed. Now, before we factor this, there's one change that we can make to the current expression. 1331 is the same thing as 11 cubed. So if we replaced 1331 with 11 cubed, the expression now becomes 11 cubed minus M cubed. And what we have here is a difference of cube terms. There's a special factor for the difference of cube terms. And that states that if you have X cubed minus Y cubed, this is going to factor two X minus Y times the quantity X squared plus X times Y plus Y squared. Here, we're going to let X equal to 11 and we're going to let Y equal to M. So if we plug in these values of X and Y into the special factor for the difference of cubes, what we get is X minus Y which is 11 minus M times the quantity X squared, which is 11 squared plus X times Y which is times M plus Y squared, which is going to be M squared. Here, 11 squared is going to evaluate to give us 100 and 11 times M is just going to give us 11 M. So once we make these simplifications, what we get is the quantity 11 minus M times 121 plus 11 M plus M squared. And this is going to be the completely factored version of the original expression. And with that being said, the answer to this problem is going to be C so I hope this video helps you in understanding how to factor the original expression. And I'll go ahead and see you all in the next video.

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Factor each polynomial. See Examples 5 and 6. 27-r^3

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