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 gives $(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$. Here, $a = 2\sqrt{t}$ and $b = 5$. Expanding gives $8t^{3/2} - 60t + 150t^{1/2} - 125$.

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 $( 2 \sqrt { t } - 5 ) ^ { 3 }$