Add or subtract.
-$$\left( - 5 x ^ { 2 } y - 8 x + 3 y ^ { 2 } \right) + \left( 7 x ^ { 2 } y - 8 x - 5 y ^ { 2 } \right)$$
A) $2 x ^ { 2 } y - 8 x - 2 y ^ { 2 }$
B) $2 x ^ { 2 } y - 16 x - 2 y ^ { 2 }$
C) $2 x ^ { 4 } y - 16 x ^ { 2 } - 2 y ^ { 2 }$
D) $- 35 x ^ { 2 } y - 8 x - 2 y ^ { 2 }$

Question

Quizplus · Accepted Answer

To add or subtract polynomials, we simply combine like terms. In this case, the like terms are the monomials with the same variables and exponents. 
$$\left( -5x^2y - 8x + 3y^2 \right) + \left(7x^2y - 8x - 5y^2 \right) = -5x^2y + 7x^2y - 8x - 8x + 3y^2 - 5y^2 = 2x^2y - 2y^2 - 16x$$ 
So the answer is B, which matches this expression after combining like terms.

Add or Subtract (−5x2y−8x+3y2)+(7x2y−8x−5y2)\left( - 5 x ^ { 2 } y - 8 x + 3 y ^ { 2 } \right) + \left( 7 x ^ { 2 } y - 8 x - 5 y ^ { 2 } \right)(−5x2y−8x+3y2)+(7x2y−8x−5y2)

Add or Subtract $\left( - 5 x ^ { 2 } y - 8 x + 3 y ^ { 2 } \right) + \left( 7 x ^ { 2 } y - 8 x - 5 y ^ { 2 } \right)$