Use the binomial theorem to expand the binomial. $$( 4 x - y ) ^ { 4 }$$
A) $256 x ^ { 4 } - 256 x ^ { 3 } y - 16 x y ^ { 3 } + y ^ { 4 }$
B) $4 x ^ { 4 } - 4 x ^ { 3 } y + 6 x ^ { 2 } y ^ { 2 } - 4 x y ^ { 3 } + y ^ { 4 }$
C) $256 x ^ { 4 } - 256 x ^ { 3 } y + 96 x ^ { 2 } y ^ { 2 } - 16 x y ^ { 3 } + y ^ { 4 }$
D) $4 x ^ { 4 } - 4 x ^ { 3 } y - 4 x y ^ { 3 } + y ^ { 4 }$

Question

Quizplus · Accepted Answer

The correct expansion using the binomial theorem for $(4x - y)^4$ is $256x^4 - 256x^3y + 96x^2y^2 - 16xy^3 + y^4$, which matches option C. This is calculated by applying the binomial coefficients (from Pascal's triangle or the combination formula $\binom{n}{k}$) and the powers of each term accordingly.

Use the Binomial Theorem to Expand the Binomial (4x−y)4( 4 x - y ) ^ { 4 }(4x−y)4

Use the Binomial Theorem to Expand the Binomial $( 4 x - y ) ^ { 4 }$