Provide an appropriate response.
-Expand the expression $\left( x - \frac { 3 } { \sqrt { x } } \right) ^ { 4 }$.
A) $x ^ { 4 } - 12 x ^ { 5 / 2 } + 54 x - \frac { 108 } { \sqrt { x } } + \frac { 81 } { x }$
B) $x ^ { 4 } - 12 x ^ { 5 / 2 } + 54 - \frac { 108 } { \sqrt { x } } + \frac { 81 } { x ^ { 2 } }$
C) $x ^ { 4 } - 12 x ^ { 5 / 2 } + 54 x - \frac { 108 } { \sqrt { x } } + \frac { 81 } { x ^ { 2 } }$
D) $x ^ { 4 } - 12 x ^ { 3 / 2 } + 54 x - \frac { 108 } { \sqrt { x } } + \frac { 81 } { x ^ { 2 } }$

Question

Quizplus · Accepted Answer

Expanding $\left( x - \frac { 3 } { \sqrt { x } } \right) ^ { 4 }$ using the binomial theorem involves calculating each term by combining the powers of $x$ and $\frac{3}{\sqrt{x}}$ appropriately. The correct expansion results in $x^4$ for the first term, $-4 \cdot 3x^{3/2}$ for the second term (which simplifies to $-12x^{5/2}$), $6 \cdot 9x$ for the third term (which simplifies to $54x$), $-4 \cdot 27/\sqrt{x}$ for the fourth term (which simplifies to $-108/\sqrt{x}$), and $81/x^2$ for the final term, making option C the correct expansion.

Provide an Appropriate Response (x−3x)4\left( x - \frac { 3 } { \sqrt { x } } \right) ^ { 4 }(x−x​3​)4

Provide an Appropriate Response $\left( x - \frac { 3 } { \sqrt { x } } \right) ^ { 4 }$