Write the binomial expansion of the expression.
-$$\left( 3 x ^ { 2 } + 2 \right) ^ { 3 }$$
A) $81 x ^ { 8 } + 27 x ^ { 6 } + 54 x ^ { 4 } + 36 x ^ { 2 } + 8$
B) $\left( 9 x ^ { 4 } + 12 x ^ { 2 } + 4 \right) ^ { 3 }$
C) $27 x ^ { 6 } + 54 x ^ { 4 } + 36 x ^ { 2 } + 8$
D) $27 x ^ { 3 } + 54 x ^ { 2 } + 36 x + 8$

Question

Quizplus · Accepted Answer

The correct expansion of $(3x^2 + 2)^3$ using the binomial theorem is $27x^6 + 54x^4 + 36x^2 + 8$, which matches option C. Each term is obtained by raising $3x^2$ and $2$ to appropriate powers and multiplying by the binomial coefficients.

Write the Binomial Expansion of the Expression (3x2+2)3\left( 3 x ^ { 2 } + 2 \right) ^ { 3 }(3x2+2)3

Write the Binomial Expansion of the Expression $\left( 3 x ^ { 2 } + 2 \right) ^ { 3 }$