Use the binomial theorem to expand the expression.
-$( x + 4 y ) ^ { 3 }$
A) $x ^ { 3 } + 64 y ^ { 3 }$
B) $x ^ { 3 } + 4 x ^ { 2 } y + 8 x y + 16 x y ^ { 2 } + 32 y ^ { 2 } + 64 y ^ { 3 }$
C) $x ^ { 3 } + 12 x ^ { 2 } y + 48 x y ^ { 2 } + 64 y ^ { 3 }$
D) $3 x + 12 y$

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 $(x + 4y)^3$, we get $x^3 + 3(x^2)(4y) + 3(x)(4y)^2 + (4y)^3$, which simplifies to $x^3 + 12x^2y + 48xy^2 + 64y^3$.

Use the Binomial Theorem to Expand the Expression (x+4y)3( x + 4 y ) ^ { 3 }(x+4y)3

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