Use the Binomial Theorem to expand and simplify the expression.
$$\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$$
A) $x ^ { 3 } + 625$
B) $x ^ { 12 } - 20 x ^ { 9 } + 150 x ^ { 6 } - 500 x ^ { 3 } + 625$
C) $x ^ { 3 } - 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } - 500 x ^ { 3 / 4 } + 625$
D) $x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625$
E) $x ^ { 12 } + 20 x ^ { 9 } + 150 x ^ { 6 } + 500 x ^ { 3 } + 625$

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 $(x^{3/4} - 5)^4$, we get terms like $x^{3}$ from $(x^{3/4})^4$, and the signs alternate because of the subtraction, leading to the correct expansion in option C.

Use the Binomial Theorem to Expand and Simplify the Expression (x3/4−5)4\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }(x3/4−5)4

Use the Binomial Theorem to Expand and Simplify the Expression $\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$