Factor by any method. See Examples 1–7. (3a+5)^2-18(3a+5)+81

Question

Accepted Answer

Hey everyone here we are asked to factor the following polynomial. Where we have the quantity of 58 plus seven squared minus 26 times the quantity of 58 plus seven plus 169. Now our first step here before we can start factoring this expression, we want to simplify by this and so we can simplify this expression by letting the variable U be equal to our first term here. Which is this quantity of five A plus seven. And so now we just want to rewrite our original expression using this variable U. So we'll have you squared minus 26. You Plus 169. And so now we looking at our simplified expression here, we see that we can apply the identity where we have X squared minus two X, Y plus Y squared which is equal to the quantity of X minus Y squared. So now we just need to rewrite our simplified expression from earlier to better match the left hand side of our formula. So before again we had U squared minus 26 U plus 169. And rewriting this expression so it matches our formula. We have U squared minus two times you times 13 plus squared. And so now looking at our rewritten expression, we see that it perfectly matches our formula. And so now we just need to compare this expression with our formula to find the values of X and Y. So we can look at our middle terms here and we see that after the coefficient of two, we have the variable X. In our formula, which means our x variable is actually equal to you in our expression. And then next to X. In our formula we have the variable Y. Well in our expression that term is 13. So we can see that Y is equal to 13. And now with these values for X and Y identified, we can go ahead and substitute it into our right hand side of the formula. And we see that our simplified expression from earlier equals the factored form according to our expression of the quantity of U minus 13 squared. And so now our last step appears to just substitute back in our original value for you which we identified earlier or declared earlier. So doing this, our factored expression now becomes the quantity of five A plus seven minus 13 squared. And now we just have to simplify our expression here and we are left with the quantity of five a minus six squared. And with this we see that there aren't any other terms of which we can factor out from this expression here. So this is our final factored form of our original expression which leaves us with answer choice D 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. (3a+5)^2-18(3a+5)+81

Key Concepts

Factoring Quadratics

Difference of Squares

Completing the Square

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