Factor each polynomial. See Examples 5 and 6. 8-a^3

Question

Accepted Answer

Hello, today we're going to be factoring the given expression. So what we are given is 125 -7 cubed. Now, before we factor this, there's one change that we can make to the current expression. 125 is the same thing as five cubed. So if we make the substitution of 125 for five cubed, what we get is five cubed minus B cubed. And what we have here is a difference of cubed terms. There's a special way to factor difference of cube terms. And that states that if you have the quantity 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 five and we're going to let Y equal to B. 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 five minus B times the quantity X squared, which is five squared plus X times Y which is going to be five B plus Y squared, which is B squared. So here there's only one simplification that we need to make and that's with five squared, five squared evaluates to 25. So once we plug in this simplification, what we get is five minus B times the quantity 25 plus five B plus B squared. And this is going to be the complete factory ization of the original expression. And with that being said, the answer to this problem is going to be A. 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.

Factor each polynomial. See Examples 5 and 6. 8-a^3

Key Concepts

Factoring Polynomials

Common Factor

Difference of Cubes

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