Multiply the polynomials by using the distributive property. $3 s ^ { 2 } t ^ { 2 } \left( s ^ { 2 } t ^ { 4 } + 6 s t ^ { 2 } + 4 s ^ { 2 } \right)$
A) $3 s ^ { 4 } t ^ { 6 } + 6 s t ^ { 2 } + 4 s ^ { 2 }$
B) $3 s ^ { 4 } t ^ { 6 } + 18 s ^ { 3 } t ^ { 4 } + 12 s ^ { 4 }$
C) $3 s ^ { 4 } t ^ { 6 } + 18 s ^ { 3 } t ^ { 4 } + 12 s ^ { 4 } t ^ { 2 }$
D) $3 s ^ { 4 } t ^ { 6 } + 6 s ^ { 3 } t ^ { 4 } + 4 s ^ { 2 }$

Question

Quizplus · Accepted Answer

To multiply the polynomials, distribute $3s^2t^2$ across each term inside the parentheses. This results in $3s^2t^2 \cdot s^2t^4 = 3s^{2+2}t^{2+4}$, $3s^2t^2 \cdot 6st^2 = 18s^{2+1}t^{2+2}$, and $3s^2t^2 \cdot 4s^2 = 12s^{2+2}t^2$, leading to the correct expression $3s^4t^6 + 18s^3t^4 + 12s^4t^2$.

Multiply the Polynomials by Using the Distributive Property 3s2t2(s2t4+6st2+4s2)3 s ^ { 2 } t ^ { 2 } \left( s ^ { 2 } t ^ { 4 } + 6 s t ^ { 2 } + 4 s ^ { 2 } \right)3s2t2(s2t4+6st2+4s2)

Multiply the Polynomials by Using the Distributive Property $3 s ^ { 2 } t ^ { 2 } \left( s ^ { 2 } t ^ { 4 } + 6 s t ^ { 2 } + 4 s ^ { 2 } \right)$