Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }$
A) $x ^ { 3 } + 1$
B) $x ^ { 3 } + 4 x ^ { 9 / 7 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$
C) $x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$
D) $- x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } - 1$
E) $x ^ { 3 } + 4 x ^ { 2 } + 6 x + 1$

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 $(x^{3/4} + 1)^4$, we get $x^3 + 4x^{9/4} + 6x^{3/2} + 4x^{3/4} + 1$, which matches choice C.

Use the Binomial Theorem to Expand and Simplify the Expression (x3/4+1)4\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }(x3/4+1)4

Use the Binomial Theorem to Expand and Simplify the Expression $\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }$