Use the binomial theorem to expand the expression.
-$( 3 x - 5 y ) ^ { 3 }$
A) $9 x ^ { 3 } y - 15 x ^ { 2 } y ^ { 2 } + 25 x y ^ { 3 }$
B) $27 x ^ { 3 } - 135 x ^ { 2 } y + 225 x y ^ { 2 } - 125 y ^ { 3 }$
C) $27 x ^ { 3 } - 45 x ^ { 2 } y + 75 x y ^ { 2 } - 125 y ^ { 3 }$
D) $9 x ^ { 3 } y - 30 x ^ { 2 } y ^ { 2 } + 25 x y ^ { 3 }$

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 $(3x - 5y)^3$, we get: $27x^3 - 3(9x^2)(5y) + 3(3x)(25y^2) - 125y^3$, simplifying to $27x^3 - 135x^2y + 225xy^2 - 125y^3$.

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

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