Use the binomial formula to expand the binomial.
-$( 4 x - 5 y ) ^ { 3 }$
A) $64 x ^ { 3 } - 80 x ^ { 2 } y + 100 x y ^ { 2 } - 125 y ^ { 3 }$
B) $64 x ^ { 3 } - 240 x ^ { 2 } y + 300 x y ^ { 2 } - 125 y ^ { 3 }$
C) $16 x ^ { 3 } y - 20 x ^ { 2 } y ^ { 2 } + 25 x y ^ { 3 }$
D) $16 x ^ { 3 } y - 40 x ^ { 2 } y ^ { 2 } + 25 x y ^ { 3 }$

Question

Quizplus · Accepted Answer

The binomial formula for the expansion of $(a + b)^n$ involves terms of the form $\binom{n}{k} a^{n-k}b^k$. Applying this to $(4x - 5y)^3$, we calculate each term: 1. $\binom{3}{0}(4x)^3(-5y)^0 = 64x^3$,2. $\binom{3}{1}(4x)^2(-5y)^1 = -240x^2y$,3. $\binom{3}{2}(4x)^1(-5y)^2 = 300xy^2$,4. $\binom{3}{3}(4x)^0(-5y)^3 = -125y^3$.Adding these terms together gives $64x^3 - 240x^2y + 300xy^2 - 125y^3$, which matches option B.

Use the Binomial Formula to Expand the Binomial (4x−5y)3( 4 x - 5 y ) ^ { 3 }(4x−5y)3

Use the Binomial Formula to Expand the Binomial $( 4 x - 5 y ) ^ { 3 }$