Use the binomial formula to expand the binomial.
-$\left( 4 x ^ { 2 } + 1 \right) ^ { 3 }$
A) $64 x ^ { 6 } + 48 x ^ { 4 } + 12 x ^ { 2 } + 1$
B) $64 x ^ { 3 } + 48 x ^ { 2 } + 12 x + 1$
C) $256 x ^ { 8 } + 64 x ^ { 6 } + 48 x ^ { 4 } + 12 x ^ { 2 } + 1$
D) $\left( 16 x ^ { 4 } + 8 x ^ { 2 } + 1 \right) ^ { 3 }$

Question

Quizplus · Accepted Answer

The binomial formula for the expansion of $(a + b)^n$ is given by $\sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. Applying this to $(4x^2 + 1)^3$, we get: $1 \cdot (4x^2)^3 + 3 \cdot (4x^2)^2 \cdot 1 + 3 \cdot (4x^2) \cdot 1^2 + 1^3 = 64x^6 + 48x^4 + 12x^2 + 1$.

Use the Binomial Formula to Expand the Binomial (4x2+1)3\left( 4 x ^ { 2 } + 1 \right) ^ { 3 }(4x2+1)3

Use the Binomial Formula to Expand the Binomial $\left( 4 x ^ { 2 } + 1 \right) ^ { 3 }$