Question

Given p(y)=9+6y^2and s(y)=3y^2−9y+6, find (p+s)(y). (p+s)(y)= Enter the expression in simplest form.

Answer 1

$\begin{gathered} \text{Given} \\ p(y)=9+6y^2 \\ s(y)=3y^2-9y+6 \end{gathered}$

Solving for (p+s)(y)

$\begin{gathered} (p+s)(y)=p(y)+s(y) \\ \\ \text{Substitute the given and we get} \\ (p+s)(y)=p(y)+s(y) \\ (p+s)(y)=(9+6y^2)+(3y^2-9y+6) \\ (p+s)(y)=9+6y^2+3y^2-9y+6 \\ (p+s)(y)=6y^2+3y^2-9y+6+9 \\ \\ \\ \text{Therefore,} \\ (p+s)(y)=9y^2-9y+15 \end{gathered}$