Factor each polynomial. See Example 7. 4(5x+7)^2+12(5x+7)+9

Question

Accepted Answer

Hey everyone here we are asked to factor the following polynomial of 36 times the quantity of three U minus seven squared plus 108 times the quantity of three U minus seven plus 81. Now our first step here in factoring this expression is to apply the identity. Where we have X squared plus two two X Y plus y squared. Which is equal to the quantity of X plus y squared. So now we just have to rewrite our original expression to better match our formula here. So we see that our original expression becomes the quantity of six times the quantity of three U minus seven squared plus two times the quantity of six times the quantity of three U minus seven times nine plus nine squared. And so now we see that our rewritten expression matches our formula. So we can start comparing the formula with the rewritten expression to find our values for X and Y. So starting with our value for X. While we can easily compare the middle term from the formula to the middle term of our exp session to find X. So we see that X is right after our two coefficient. So X is going to be six times the quantity of three U minus seven. And now finding our value for Y, we see that. Why is the term right next to X here in our middle term? So why is just going to be nine? And so now since we have our X and Y values identified, we can go ahead and just substitute them into the factored the factored form the right hand side of our formula to find the factored form of our original expression. So again from our original expression we had 36 times the quantity of three U minus seven squared plus 108 times each quantity of three U minus seven plus 81. And now from our formula we see that this expression is equivalent to the quantity of six times the quantity of three U minus seven plus nine squared. And so now we just have to simplify our factored expression here by factoring in this six. So we have the quantity of U minus 40 to plus nine all squared. And so now just adding the like terms together we have our final simplified expression of the quantity of 18 U minus 30 three squared. And so now there aren't any other terms that we can factor out. So this is the final factored form of our original expression which is answer choice B Thanks for watching. I hope you found this video helpful and I'll see you again next time

Factor each polynomial. See Example 7. 4(5x+7)^2+12(5x+7)+9

Key Concepts

Factoring Polynomials

Substitution Method

Quadratic Form

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