Factor each polynomial. See Examples 5 and 6.

Question

y^{2} - x^{2} + 12 x - 36

Accepted Answer

Hello, today we're going to be factoring the given polynomial. So what we are given is U squared minus V squared plus V minus 441. Now, the first thing we can go ahead and do is group up the last three terms together. And when we do this, we want the first term to be positive. In order to turn negative the square positive, we're going to have to factor out a negative one from the entire quantity. Doing this is going to give us U squared minus the quantity V squared minus 42 V plus 441. Now, V squared minus 42 V plus 441 is a fact, Herbal Trin Amiel as this quantity is going to factor two V minus 21 squared. So once we make this substitution, we get you squared minus the quantity the -21 squared. Now, what we have here is a difference of squares and the difference of square states that if you have the quantity 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 equal to you and we're going to let y equal to the quantity V -21. So once we plug in these values for X and Y into the difference of squares, what we end up getting is X plus Y, which is going to be U plus V minus 21 times the quantity X minus Y which is going to be U minus the quantity V minus 21. There's only one simplification we need to do here. And that's going to be to distribute the negative one into V minus 21. And once we do that, we get U plus V minus 21 times the quantity U minus V plus 21. And this is going to be the completely factored form of the original expression. And with that being said, the answer to this problem is going to be be. So I hope this video helps you in understanding how to use factor the difference of squares. And I'll go ahead and see you all in the next video.

Factor each polynomial. See Examples 5 and 6. $y^{2} - x^{2} + 12 x - 36$

Key Concepts

Polynomial Factoring

Difference of Squares

Completing the Square

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