# Add the two polynomials. (-3y^{4}+6y^{2}+7) and (10y^{4}-7y^{2}-2y-4)

$\left(-3{y}^{4}+6{y}^{2}+7\right)$ and $\left(10{y}^{4}-7{y}^{2}-2y-4\right)$
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Step 1
We need to add the following two polynomials
$\left(-3{y}^{4}+6{y}^{2}+7\right)$ and $\left(10{y}^{4}-7{y}^{2}-2y-4\right)$
Step 2
The polynomials can be added and simplified as following
$\left(-3{y}^{4}+6{y}^{2}+7\right)+\left(10{y}^{4}-7{y}^{2}-2y-4\right)=-3{y}^{4}+6{y}^{2}+7+10{y}^{4}-7{y}^{2}-2y-4$
$=\left(-3{y}^{4}+10{y}^{4}\right)+\left(6{y}^{2}-7{y}^{2}\right)-2y+7-4$
$=\left(-3+10\right){y}^{4}+\left(6-7\right){y}^{2}-2y+3$
$=7{y}^{4}-{y}^{2}-2y+3$
Hence, $\left(-3{y}^{4}+6{y}^{2}+7\right)+\left(10{y}^{4}-7{y}^{2}-2y-4\right)=7{y}^{4}-{y}^{2}-2y+3$

Hector Roberts