Work each problem. Match each polynomial in Column I with its ...

Question

Work each problem. Match each polynomial in Column I with its factored form in Column II.

Polynomials in Column I matched with their factored forms in Column II for a factoring exercise.

Accepted Answer

Hey everyone here we are asked to find the factored form of 64 C cubed plus 343. So here the first thing we need to notice with this expression is that both of our terms here are perfect cubes. We can see that 64 C cubed is equivalent to the quantity of four C cubed. And our second term here, this 343 is equivalent to seven cubed. So now with these two rewritten terms we can rewrite our original expression as the quantity of four C cubed plus seven cubed. And now here we can clearly see that we have the sum of two cubes. So we need to recall the sum of cubes formula which tells us that X cubed plus Y cubed is equivalent to the quantity of X plus y times the quantity of X squared minus x times Y plus y squared. And now we can just identify our X and Y terms in relation to our rewritten expression here. So we can see our first term is going to be our values for X. So X is going to be four C. And then our second cube term is our Y. So y is going to be seven. And now we can use this the sum of cubes formula formula to factor out our expression. So again we have the quantity of four C cubed plus seven cubed. And now rewriting this expression, we have the quantity of four C plus seven times the quantity of The quantity of four seek squared minus four C times seven plus seven squared. And now all that is left to do is to simplify some of our terms here in our factored expression. So now we have the simplified factored expression of the quantity of four C plus seven times the quantity of 16 C squared minus C plus 49. And with this we have finished factoring our original expression. Therefore we are left with answer choice B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Work each problem. Match each polynomial in Column I with its factored form in Column II.

Key Concepts

Sum and Difference of Cubes

Identifying 'a' and 'b' in Cubic Expressions

Matching Factored Forms to Original Polynomials

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