Expand a Binomial Raised to a Power
-$$\left( x ^ { 2 } - 5 y \right) ^ { 4 }$$
A) $x ^ { 8 } - 20 x ^ { 6 } y + 150 x ^ { 4 } y ^ { 2 } - 500 x ^ { 2 } y ^ { 3 } + 625 y ^ { 4 }$
B) $x ^ { 8 } - 5 x ^ { 6 } y + 150 x ^ { 4 } y ^ { 2 } - 250 x ^ { 2 } y ^ { 3 } + 625 y ^ { 4 }$
C) $x ^ { 4 } - 20 x ^ { 3 } y + 150 x ^ { 2 } y ^ { 2 } - 500 x y ^ { 3 } + 625 y ^ { 4 }$
D) $x ^ { 8 } - 20 x ^ { 6 } y + 150 x ^ { 4 } y ^ { 2 } + 20 x ^ { 2 } y ^ { 3 } + 625 y ^ { 4 }$

Question

Quizplus · Accepted Answer

The correct expansion is found using the binomial theorem, which involves calculating each term by combining the coefficients from Pascal's triangle with the powers of each part of the binomial raised to the appropriate power. The correct coefficients for the expansion of $(x^2 - 5y)^4$ are 1, -20, 150, -500, and 625, corresponding to the powers of $x^8$, $x^6y$, $x^4y^2$, $x^2y^3$, and $y^4$, respectively.

Expand a Binomial Raised to a Power - (x2−5y)4\left( x ^ { 2 } - 5 y \right) ^ { 4 }(x2−5y)4

Expand a Binomial Raised to a Power
- $\left( x ^ { 2 } - 5 y \right) ^ { 4 }$