Write the binomial expansion of the expression.
-$$\left( \frac { 1 } { x } - \sqrt { 7 } y \right) ^ { 3 }$$
A) $\frac { 1 } { x ^ { 3 } } + \frac { 3 \sqrt { 7 } y } { x ^ { 2 } } + \frac { 21 y ^ { 2 } } { x } + 7 \sqrt { 7 } y ^ { 3 }$
B) $\frac { 1 } { x ^ { 3 } } - \frac { 3 \sqrt { 7 } y } { x ^ { 2 } } + \frac { 21 y ^ { 2 } } { x } - 7 \sqrt { 7 } y ^ { 3 }$
C) $\frac { 1 } { x ^ { 3 } } - \frac { 3 \sqrt { 7 } y } { x ^ { 2 } } + \frac { 63 y ^ { 2 } } { x } - 7 \sqrt { 7 } y ^ { 3 }$
D) $\frac { 1 } { x ^ { 3 } } - \frac { 3 \sqrt { 7 } y } { x ^ { 2 } } - \frac { 21 y ^ { 2 } } { x } - 7 \sqrt { 7 } y ^ { 3 }$

Question

Quizplus · Accepted Answer

The correct expansion follows the binomial theorem $(a - b)^n$, where $a = \frac{1}{x}$ and $b = \sqrt{7}y$. Each term alternates in sign, and the coefficients follow the pattern of binomial coefficients (1, 3, 3, 1) multiplied by the respective powers of $a$ and $b$.

Write the Binomial Expansion of the Expression (1x−7y)3\left( \frac { 1 } { x } - \sqrt { 7 } y \right) ^ { 3 }(x1​−7​y)3

Write the Binomial Expansion of the Expression $\left( \frac { 1 } { x } - \sqrt { 7 } y \right) ^ { 3 }$