Factor each polynomial. See Example 7. 9(a-4)^2+30(a-4)+25

Question

Accepted Answer

Hey everyone here we are asked to factor the following polynomial of 16 times the quantity of eight plus six squared plus 56 times the quantity of a plus six plus 49. 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 our next step is to just rewrite our given expression so that it better matches our formula. So our original expression becomes the quantity of four times the quantity of a plus six squared plus two times the quantity of four times the quantity of eight plus six times seven plus seven squared. And so now looking at our rewritten expression, we see that it matches our formula here. So we can now just compare the two expressions to find our values for X and Y. So starting with our value for X. Well from our for our formula we see that X is the first term from our expression. So in this case X is going to be four times the quantity of a plus six. And now from our formula we see that Y is our third term here. So why is going to just be seven And now with our X and Y values identified, we can go ahead and just substitute them into 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 have 16 times the quantity of eight plus six school plus 56 times the quantity of eight plus six plus 49. And now from our formula, we know that this expression here is equivalent to the Factored form where we have the quantity of four times the quantity of a plus six plus seven all squared. And so now we just have to factor or sorry, simplify our expression by factoring in this four here. So our expression becomes the quantity of for a plus 24 plus seven squared. And now just adding our terms together here our like terms together we have our final factored expression of the quantity of four A plus 31 squared. And so now looking at our factored expression, we can see that there aren't any other terms of which we can factor out. Therefore this is our final answer here, which is answer choice. A thanks for watching. I hope you found this video helpful. And I'll see you again next time.

Factor each polynomial. See Example 7. 9(a-4)^2+30(a-4)+25

Key Concepts

Factoring Polynomials

Perfect Square Trinomials

Substitution in Polynomials

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