Use the Binomial Theorem to expand and simplify the expression. $( 2 \sqrt { t } - 5 ) ^ { 3 }$
A) $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } - 125$
B) $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } + 125$
C) $8 t ^ { 3 / 2 } - 60 t - 150 t ^ { 1 / 2 } - 125$
D) $8 t ^ { 3 / 2 } + 60 t + 150 t ^ { 1 / 2 } + 125$
E) $8 t ^ { 3 / 2 } + 60 t - 150 t ^ { 1 / 2 } - 125$

Question

Use the Binomial Theorem to expand and simplify the expression.  $( 2 \sqrt { t } - 5 ) ^ { 3 }$  
A) $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } - 125$
B) $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } + 125$
C) $8 t ^ { 3 / 2 } - 60 t - 150 t ^ { 1 / 2 } - 125$
D) $8 t ^ { 3 / 2 } + 60 t + 150 t ^ { 1 / 2 } + 125$
E) $8 t ^ { 3 / 2 } + 60 t - 150 t ^ { 1 / 2 } - 125$

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 $(2\sqrt{t} - 5)^3$, we get: $8t^{3/2} - 3 \cdot 8t^{1/2} \cdot 5 + 3 \cdot 2t^{0} \cdot 25 - 125$, which simplifies to $8t^{3/2} - 60t + 150t^{1/2} - 125$.

Use the Binomial Theorem to Expand and Simplify the Expression (2t−5)3( 2 \sqrt { t } - 5 ) ^ { 3 }(2t​−5)3

Use the Binomial Theorem to Expand and Simplify the Expression $( 2 \sqrt { t } - 5 ) ^ { 3 }$