Use the Binomial Theorem to expand the binomial.
-$$( 2 x - 2 y ) ^ { 3 }$$
A) $8 x ^ { 3 } - 24 x ^ { 2 } y + 24 x y ^ { 2 } - 8 y ^ { 3 }$
B) $4 x ^ { 3 } y - 8 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$
C) $4 x ^ { 3 } y - 4 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$
D) $8 x ^ { 3 } - 8 x ^ { 2 } y + 8 x y ^ { 2 } - 8 y ^ { 3 }$

Question

Quizplus · Accepted Answer

The Binomial Theorem states that $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. Applying this to $(2x - 2y)^3$, we get $8x^3 - 24x^2y + 24xy^2 - 8y^3$, which matches choice A.

Use the Binomial Theorem to Expand the Binomial (2x−2y)3( 2 x - 2 y ) ^ { 3 }(2x−2y)3

Use the Binomial Theorem to Expand the Binomial $( 2 x - 2 y ) ^ { 3 }$