Expand the expression using the Binomial Theorem.
-$$( 3 x - 2 y ) ^ { 3 }$$
A) $9 x ^ { 3 } y - 12 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$

B) $27 x ^ { 3 } - 54 x ^ { 2 } y + 36 x y ^ { 2 } - 8 y ^ { 3 }$

C) $9 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$

D) $27 x ^ { 3 } - 18 x ^ { 2 } y + 12 x y ^ { 2 } - 8 y ^ { 3 }$

Question

Expand the expression using the Binomial Theorem.
-$$( 3 x - 2 y ) ^ { 3 }$$
A) $9 x ^ { 3 } y - 12 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$

B) $27 x ^ { 3 } - 54 x ^ { 2 } y + 36 x y ^ { 2 } - 8 y ^ { 3 }$

C) $9 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 }$

D) $27 x ^ { 3 } - 18 x ^ { 2 } y + 12 x y ^ { 2 } - 8 y ^ { 3 }$

Quizplus · Accepted Answer

The Binomial Theorem for the expansion of $(a + b)^n$ gives us each term in the form of $\binom{n}{k} a^{n-k} b^k$, where $\binom{n}{k}$ is the binomial coefficient. For $(3x - 2y)^3$, we have $n = 3$ and the terms are:- First term: $\binom{3}{0} (3x)^3 (-2y)^0 = 27x^3$- Second term: $\binom{3}{1} (3x)^2 (-2y)^1 = -54x^2y$- Third term: $\binom{3}{2} (3x)^1 (-2y)^2 = 36xy^2$- Fourth term: $\binom{3}{3} (3x)^0 (-2y)^3 = -8y^3$Combining these gives the expansion $27x^3 - 54x^2y + 36xy^2 - 8y^3$.

Expand the Expression Using the Binomial Theorem (3x−2y)3( 3 x - 2 y ) ^ { 3 }(3x−2y)3

Expand the Expression Using the Binomial Theorem $( 3 x - 2 y ) ^ { 3 }$