Factor by any method. See Examples 1–7. (x+y)^2-(x-y)^2

Question

Accepted Answer

Hey everyone here we are asked to factor the following polynomial of the quantity of two A plus three B squared minus the quantity of two a minus three B squared. So looking at this expression here, we see that we have the difference of two squares. So we need to recall the difference of squares formula where we have x squared minus Y squared is equal to the quantity of X plus y times the quantity of x minus Y. And now our next step is to just compare our formula here with our given expression to find our values for X and Y. So starting with finding our value for X. Well from the formula we see that X squared is our first squared term from our expression. So we see that X squared is the quantity of two A plus three B squared, which tells us that the value for X is just two A plus three B. And now we can move on to finding our value for Y. Well, again from our formula, we see that y squared is going to be our second squared term from our expression. So we see that y squared is the quantity of two a minus three B squared. Which tells us that the value for y is just to a minus three B. So now that we have identified the values for X and Y. We can go ahead and substitute them into the right hand side of our formula. So doing this, we see that our original expression which was the quantity of two A plus three B squared minus the quantity of two a minus three B squared. We see that the factored form of this expression according to our formula is the quantity of two A plus three B plus two A. Plus to a minus three B. Times the quantity of two A plus three B minus the quantity of two A minus three B. So now we just have to make some simplifications here to our expression. And we see that our factored form of our original expression turns out to be the quantity of four A. Times the quantity of six B. Which multiplying these terms together, we see that our final factored form is just 24 A. B. And now there aren't any other terms to factor. Therefore our final answer is just 24 A. B. Which is the final factored form of our original expression here, which is answer choice. A Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Struggling with College Algebra?

Factor by any method. See Examples 1–7. (x+y)^2-(x-y)^2

Watch next

Factoring Polynomials practice set