Question

what is the additive inverse of the polynomial?
$-7y^{2}+x^{2}y - 3xy - 7x^{2}$
$\bigcirc$ $7y^{2}-x^{2}y + 3xy + 7x^{2}$
$\bigcirc$ $7y^{2}+x^{2}y + 3xy + 7x^{2}$
$\bigcirc$ $-7y^{2}-x^{2}y - 3xy - 7x^{2}$
$\bigcirc$ $7y^{2}+x^{2}y - 3xy - 7x^{2}$

Explanation:

Step1: Define additive inverse

The additive inverse of a polynomial $P$ is $-P$, which means multiplying each term by $-1$.

Step2: Apply to each term

Take the polynomial $-7y^2 + x^2y - 3xy - 7x^2$, multiply each term by $-1$:
$(-1)(-7y^2) + (-1)(x^2y) + (-1)(-3xy) + (-1)(-7x^2)$

Step3: Simplify each term

Calculate each product:
$7y^2 - x^2y + 3xy + 7x^2$

Answer:

A. $7y^2 - x^2y + 3xy + 7x^2$