Factor each polynomial completely. See Example 6. 25s⁴ - 9t²

Question

Accepted Answer

Welcome back. I am so glad you're here. We're asked to rewrite the following expression by factoring it completely. Our expression is 16 A raised to the fourth power minus 121 B squared. Our answer choices are answer choice. A, the quantity of 11 A squared plus four B multiplied by the quantity of 11 A squared minus four B. Answer choice B, the quantity of four A squared plus 11 B squared. Answer choice C, the quantity of four A squared plus 11 B multiplied by the quantity of four A squared minus 11 B and answer choice D, the quantity of 11 A plus four B squared squared. All right. So we take a look at our expression and everything there looks like it could be a square. So we might be dealing with a difference of squares here. Let's see if we are. So we recall from previous lessons that a difference of squares is given to us in A squared minus B squared. So A squared, that's the first thing. If 16 A race to the fourth power is our A squared, then what's our A going to be? So what's being squared? In order to get 16, that's four. And what's being squared in order to get a raise to the fourth power? That's A squared. Now, let's take a look at the term being subtracted. That's our B squared. Well, B squared is 121 B squared. What would our B be? Well, to get 121 we're scoring 11 and to get B squared, we're squaring B so B equals 11 B and so that means because we do have a difference of squares, we can factor this pretty quickly. We recall from previous lessons that A squared minus B squared factors out to B, the quantity of A plus B multiplied by the quantity of A minus B. So we just need to fill in our A S and BS. So we set our expression equal to the quantity of, instead of A, we have four A squared plus instead of B, we have 11 B and that's multiplied by the quantity of, instead of A four A squared and then minus instead of B 11 B. And that's as factored as that one can get, we look at our answer choices and this matches with answer choice. See, well done. We'll catch you on the next one.

Factor each polynomial completely. See Example 6. 25s⁴ - 9t²

Key Concepts

Difference of Squares

Factoring Higher Powers

Prime Factorization of Coefficients

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