Question

perform the indicated operation.
subtract ((5y^2 - 7y - 4)) from the sum of ((3y^2 + 9)) and ((4y + 2)).
((5y^2 - 7y - 4)) subtracted from the sum of ((3y^2 + 9)) and ((4y + 2)) is (square).
(do not factor.)

Explanation:

Step1: Find the sum of \((3y^2 + 9)\) and \((4y + 2)\)

To find the sum, we add the two expressions: \((3y^2 + 9)+(4y + 2)\). Combine like terms: the \(y^2\) term is \(3y^2\), the \(y\) term is \(4y\), and the constant terms are \(9 + 2 = 11\). So the sum is \(3y^2+4y + 11\).

Step2: Subtract \((5y^2 - 7y - 4)\) from the sum

We need to compute \((3y^2+4y + 11)-(5y^2 - 7y - 4)\). Distribute the negative sign to each term in the second polynomial: \(3y^2+4y + 11-5y^2 + 7y + 4\).

Step3: Combine like terms

For the \(y^2\) terms: \(3y^2-5y^2=-2y^2\). For the \(y\) terms: \(4y + 7y = 11y\). For the constant terms: \(11 + 4 = 15\). So the result is \(-2y^2+11y + 15\).

Answer:

\(-2y^2 + 11y + 15\)