Expand the expression using the Binomial Theorem.
-$$\left( 4 x ^ { 2 } - 1 \right) ^ { 3 }$$
A) $64 x ^ { 3 } - 48 x ^ { 2 } + 12 x - 1$
B) $64 x ^ { 6 } - 48 x ^ { 4 } + 12 x ^ { 2 } - 1$
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 Theorem states that $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. Applying this to $(4x^2 - 1)^3$, we get $64x^6 - 48x^4 + 12x^2 - 1$, which matches option B.

Expand the Expression Using the Binomial Theorem (4x2−1)3\left( 4 x ^ { 2 } - 1 \right) ^ { 3 }(4x2−1)3

Expand the Expression Using the Binomial Theorem $\left( 4 x ^ { 2 } - 1 \right) ^ { 3 }$