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

Question

Work each problem. Match each polynomial in Column I with its factored form in Column II.  a. x^2 + 10xy +25y^2 b. x^2-10xy +25y^2 c.x^2-25y^2 d. 25y^2-x^2  A. (x+5y ) (x-5y) B. (x+5y)^2 C. (x-5y)^2 D. (5y+x)(5y-x)

Accepted Answer

Hey everyone here we are asked to find the factored form of the expression A squared minus 20 for a B plus 144 B squared. Now our first step in factoring this expression, we want to identify the terms which are perfect squares. Now we can see here that our first term which is a squared, this is in fact a perfect square and we can rewrite it as the quantity of a squared. And next our other perfect square in this expression is our third term which is 144 B squared. And we can rewrite this term as the quantity of B squared. And now with these rewritten terms here we can use them and rewrite our original expression as the quantity of a squared minus 20 for a B plus the quantity of 12 B squared. And now looking at our rewritten expression, we can see that we have a perfect square trin Amiel, which means we need to recall the formulas for a perfect square trin Amiel. And we have two formulas here. So the first formula is x squared plus two, Xy plus y squared is equal to the quantity of x plus y squared. In our second formula we have x squared minus two, X, Y plus y squared is equal to the quantity of x minus y squared. And now looking at our rewritten expression, we can see our middle term has a negative sign and we can see that this matches our second formula which also has a negative sign for the middle term. And therefore we know we need to use this second formula. So now we can just identify our X and Y terms in relation to our expression here so we can see that X. Is going to be A. And then that means Y is going to be 12 B. So now plugging in these values into our formula, we have a squared minus two times a, times 12 B plus the quantity of 12 B squared. And now again with our formula, we know that this expression here is equal to the quantity of a minus 12 B, all squared. And with this we have found our final factored expression and 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.

Struggling with College Algebra?

Work each problem. Match each polynomial in Column I with its factored form in Column II. a. x^2 + 10xy +25y^2 b. x^2-10xy +25y^2 c.x^2-25y^2 d. 25y^2-x^2 A. (x+5y ) (x-5y) B. (x+5y)^2 C. (x-5y)^2 D. (5y+x)(5y-x)

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