Factor by any method. See Examples 1–7. 4z^2+28z+49

Question

Accepted Answer

Hey everyone here we are asked to factor the following polynomial of 25 A squared plus 140 A plus 196. Now, our first step here in factoring this expression is to apply the identity where we have x squared plus two, xy plus Y squared, which is equal to the quantity of X plus y squared. So now before we can start utilizing this formula, we need to rewrite our original expression so that it better matches our formula. So doing this, our original expression becomes the quantity of five A squared plus two times the quantity of five a times 14 plus 14 squared. So now we see that our rewritten expression perfectly match which is our formula here. So we can easily find our our values for X and Y. So starting with our value for X, what we see from the formula that our first term is X squared. So our value for X is going to be five A. And also from our formula, we see that our last term is y squared. So we know that Y is just going to be 14. And so now that we have our X and Y values clearly identified, we can just substitute them into the factored form from our formula or the right hand side of our formula. And we see that our original expression which was 25 a squared plus 140 A plus 196 takes the factored form according to our formula of the quantity of five A plus 14 squared. And with this we looking at our factored expression here, we see that there aren't any other terms which we can factor out. So we see that this is our final factored form of our original expression, which is answer choice. A 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. 4z^2+28z+49

Key Concepts

Factoring Quadratic Expressions

Perfect Square Trinomials

The Distributive Property

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