Expand a Binomial Raised to a Power
-$$\left( x ^ { 2 } - 3 y \right) ^ { 4 }$$
A) $x ^ { 8 } - 12 x ^ { 6 } y + 54 x ^ { 4 } y ^ { 2 } - 108 x ^ { 2 } y ^ { 3 } + 81 y ^ { 4 }$
B) $x ^ { 8 } - 3 x ^ { 6 } y + 54 x ^ { 4 } y ^ { 2 } - 54 x ^ { 2 } y ^ { 3 } + 81 y ^ { 4 }$
C) $x ^ { 4 } - 12 x ^ { 3 } y + 54 x ^ { 2 } y ^ { 2 } - 108 x y ^ { 3 } + 81 y ^ { 4 }$
D) $x ^ { 8 } - 12 x ^ { 6 } y + 54 x ^ { 4 } y ^ { 2 } + 12 x ^ { 2 } y ^ { 3 } + 81 y ^ { 4 }$

Question

Quizplus · Accepted Answer

The correct expansion of $(x^2 - 3y)^4$ is obtained using the binomial theorem, which involves calculating each term by combining the coefficients from Pascal's triangle with the appropriate powers of $x^2$ and $-3y$. The correct coefficients for the expansion are 1, -12, 54, -108, and 81, leading to the correct expansion as given in option A.

Expand a Binomial Raised to a Power - (x2−3y)4\left( x ^ { 2 } - 3 y \right) ^ { 4 }(x2−3y)4

Expand a Binomial Raised to a Power
- $\left( x ^ { 2 } - 3 y \right) ^ { 4 }$