Factor each polynomial. See Examples 5 and 6.

Question

9 m^{2} - n^{2} - 2 n - 1

Accepted Answer

Hello, today we're going to be factoring the given expression. So what we are given is 25 D squared minus E squared minus 14 E minus 49. So what we can go ahead and do is group up the last three terms together. Now we want the first term to be positive. So we're gonna go ahead and factor out negative one from the last three terms doing. This is going to give us 25 D squared minus E squared plus 14 E plus and E squared plus 14 E plus 49 is a factory built Rhino Meal as if factors to E plus seven squared. So if we replace that quantity with E plus seven squared, the expression becomes 25 D squared minus the quantity E plus seven squared. And there's one more substitution that we can do with the current expression. And that's with 25 D squared because 25 D squared can be rewritten as five D squared. So once we make the substitution, the expression now becomes five D squared minus the quantity E plus seven squared. And if you notice what we currently have is a difference of squares. And there's a special factor for the difference of squares. If you have X squared minus Y squared, this is going to factor two X plus Y times X minus Y. Here, we're going to let X to equal to five D and we're going to let Y equal to the quantity E plus seven. So once we plug in these values for X and Y into the difference of squares, what we get is X plus Y, which is five D plus E plus seven times the quantity X minus Y, which is going to be five D minus the quantity E plus seven. So there's only one simplification we need to make here and that's to distribute the negative one into E plus seven. And doing this is going to give us five D plus E plus seven times the quantity five D minus E minus seven. 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 this expression. And I'll go ahead and see you all in the next video.

Factor each polynomial. See Examples 5 and 6. $9 m^{2} - n^{2} - 2 n - 1$

Key Concepts

Factoring Polynomials

Difference of Squares

Rearranging and Grouping Terms

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