Expand a Binomial Raised to a Power
-$\left( x ^ { 5 } + 4 y \right) ^ { 4 }$
A) $x ^ { 20 } + 16 x ^ { 15 } y + 96 x ^ { 10 } y ^ { 2 } + 256 x ^ { 5 } y ^ { 3 } + 256 y ^ { 4 }$
B) $x ^ { 9 } + 12 x ^ { 8 } y + 96 x ^ { 7 } y ^ { 2 } + 192 x ^ { 5 } y ^ { 3 } + 256 y ^ { 4 }$
C) $x ^ { 9 } + 16 x ^ { 8 } y + 24 x ^ { 7 } y ^ { 2 } + 16 x ^ { 5 } y ^ { 3 } + 4 y ^ { 4 }$
D) $x ^ { 20 } + 12 x + 15 y + 96 x ^ { 10 } y ^ { 2 } + 192 x ^ { 5 } y ^ { 3 } + 256 y ^ { 4 }$

Question

Quizplus · Accepted Answer

The correct expansion of $(x^5 + 4y)^4$ is obtained using the binomial theorem, which involves calculating each term by combining the powers of $x^5$ and $4y$ appropriately and using the binomial coefficients. The correct expansion is $x^{20} + 16x^{15}y + 96x^{10}y^2 + 256x^5y^3 + 256y^4$, matching option A.

Expand a Binomial Raised to a Power - (x5+4y)4\left( x ^ { 5 } + 4 y \right) ^ { 4 }(x5+4y)4

Expand a Binomial Raised to a Power
- $\left( x ^ { 5 } + 4 y \right) ^ { 4 }$