Use the binomial theorem to expand the expression.
-$\left( x ^ { 3 } + 2 y \right) ^ { 4 }$
A) $x ^ { 7 } + 6 x ^ { 6 } y + 24 x ^ { 5 } y ^ { 2 } + 24 x ^ { 3 } y ^ { 3 } + 16 y ^ { 4 }$
B) $x ^ { 12 } + 8 x ^ { 9 } y + 24 x ^ { 6 } y ^ { 2 } + 32 x ^ { 3 } y ^ { 3 } + 16 y ^ { 4 }$
C) $x ^ { 7 } + 8 x ^ { 6 } y + 12 x ^ { 5 } y ^ { 2 } + 8 x ^ { 3 } y ^ { 3 } + 2 y ^ { 4 }$
D) $x ^ { 12 } + 6 x ^ { 9 } y + 24 x ^ { 6 } y ^ { 2 } + 24 x ^ { 3 } y ^ { 3 } + 16 y ^ { 4 }$

Question

Quizplus · Accepted Answer

The correct expansion using the binomial theorem is $x^{12} + 8x^9y + 24x^6y^2 + 32x^3y^3 + 16y^4$, which matches choice B. The coefficients are determined by the binomial coefficients for the expansion of $(a + b)^n$, where $n=4$ in this case, and $a=x^3$, $b=2y$.

Use the Binomial Theorem to Expand the Expression (x3+2y)4\left( x ^ { 3 } + 2 y \right) ^ { 4 }(x3+2y)4

Use the Binomial Theorem to Expand the Expression $\left( x ^ { 3 } + 2 y \right) ^ { 4 }$