Simplify the polynomial by combining like terms.
-$$\left( 5 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 6 x y \right) + \left( 3 x ^ { 5 } y ^ { 3 } + 11 x ^ { 3 } y + 12 x y \right)$$
A) $8 x ^ { 5 } y ^ { 3 } + 21 x ^ { 3 } y ^ { 2 } + 18 x y$
B) $8 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 11 x ^ { 3 } y + 18 x y$
C) $8 x ^ { 5 } y ^ { 3 } + 21 x ^ { 3 } y + 18 x y$
D) $21 x ^ { 6 } y ^ { 3 } + 8 x ^ { 5 } y ^ { 3 } + 18 x y$

Question

Quizplus · Accepted Answer

Combining like terms, we add coefficients of terms with the same powers of x and y. $5x^5y^3 + 3x^5y^3 = 8x^5y^3$, $10x^3y^2$ remains unchanged as there's no similar term, $11x^3y$ also remains unchanged for the same reason, and $6xy + 12xy = 18xy$.

Simplify the Polynomial by Combining Like Terms (5x5y3+10x3y2+6xy)+(3x5y3+11x3y+12xy)\left( 5 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 6 x y \right) + \left( 3 x ^ { 5 } y ^ { 3 } + 11 x ^ { 3 } y + 12 x y \right)(5x5y3+10x3y2+6xy)+(3x5y3+11x3y+12xy)

Simplify the Polynomial by Combining Like Terms $\left( 5 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 6 x y \right) + \left( 3 x ^ { 5 } y ^ { 3 } + 11 x ^ { 3 } y + 12 x y \right)$