Question

add the following polynomial expressions:
$(-4y^2 + 3y - 2x^3) + (-2x^3 - y - y^2)$
a $5y^2 + 2y$
b $3y^2 + 2y - 4x^3$
c $5y^2 + 4y - 4x^3$
d $-5y^2 + 2y - 4x^3$

Explanation:

Step1: Remove parentheses

To add the polynomial expressions, we first remove the parentheses. The expression becomes:
$-4y^{2}+3y - 2x^{3}-2x^{3}-y - y^{2}$

Step2: Combine like terms for \(x^{3}\) terms

The terms with \(x^{3}\) are \(-2x^{3}\) and \(-2x^{3}\). Combining them:
\(-2x^{3}-2x^{3}=-4x^{3}\)

Step3: Combine like terms for \(y^{2}\) terms

The terms with \(y^{2}\) are \(-4y^{2}\) and \(-y^{2}\). Combining them:
\(-4y^{2}-y^{2}=-5y^{2}\)

Step4: Combine like terms for \(y\) terms

The terms with \(y\) are \(3y\) and \(-y\). Combining them:
\(3y - y = 2y\)

Step5: Combine all combined terms

Putting together the combined terms for \(x^{3}\), \(y^{2}\), and \(y\), we get:
\(-5y^{2}+2y - 4x^{3}\)

Answer:

D. \(-5y^{2}+2y - 4x^{3}\)