Question

which expression is equivalent to this polynomial expression?
$(8x^{2}y^{2}-9x^{2}y + 9y)-(6x^{2}y-xy^{2}+4y)$
a. $-7x^{2}y^{2}+xy^{2}+5y$
b. $8x^{2}y^{2}-3x^{2}y-xy^{2}+13y$
c. $8x^{2}y^{2}-15x^{2}y+xy^{2}+5y$
d. $-7x^{2}y^{2}-xy^{2}+13y$

Explanation:

Step1: Distribute the negative sign

$(8x^2y^2 - 9x^2y + 9y) - 6x^2y + xy^2 - 4y$

Step2: Combine like $x^2y$ terms

$8x^2y^2 + (-9x^2y - 6x^2y) + xy^2 + 9y - 4y$
$8x^2y^2 - 15x^2y + xy^2 + 9y - 4y$

Step3: Combine constant $y$ terms

$8x^2y^2 - 15x^2y + xy^2 + (9y - 4y)$
$8x^2y^2 - 15x^2y + xy^2 + 5y$

Answer:

C. $8x^2y^2 - 15x^2y + xy^2 + 5y$