Factor by any method. See Examples 1–7.

Question

1000 x cubed plus 343 y cubed

Accepted Answer

Hey everyone here we are asked to factor the following polynomial of 1331 A cubed plus 729 B cubed. So now our first step before we can start factoring this expression, we need to apply the identity where we have X cubed plus Y cubed is equal to the quantity of X plus Y, times X. Quantity of X squared minus x, Y plus y squared. Now our next step is to rewrite our original expression so that it better matches our formula. And so doing this we need to rewrite both of our terms from our original expression as cubes. So doing this, our original expression becomes the quantity of 11 A. Q plus the quantity of nine B cubed. So with this we can see that our rewritten expression easily matches our formula here. So now we can just identify our values for X and Y by comparing the expression with the formula. So starting with our value for X. Well from the formula we see that X is going to be our first term which in this case in our expression it is 11 A. And for our value for Y. Well from the formula we see that Y is the second term from our expression. So we see that Y is going to be nine B. And now that we have our values for X. And y identified, 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 is 1331 A. Cute plus 729 B cubed. We see that this expression takes the factored form according to our formula of the quantity of A plus nine B times the quantity of the quantity of 11 A squared minus the quantity of 11 A. Times the quantity of nine B plus the quantity of nine B squared. So with this we just have to start simplifying our factored form here. And we see that we have the factored form of the quantity of A plus nine B. Times the quantity of 121 A squared minus 99 A. B plus 81 B squared. And with this looking at our factored expression here, we can see that there aren't any other terms of which we can factor out. Therefore this is our final factored factored form of our original expression which leaves us with answer choice C. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Factor by any method. See Examples 1–7. $1000 x cubed plus 343 y cubed$

Key Concepts

Sum of Cubes Formula

Identifying Perfect Cubes

Factoring Polynomials

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