Write the first three terms of the expansion.
-$( 3 x + 2 y ) ^ { 8 }$
A) $6561 x ^ { 8 } y + 34,992 x ^ { 7 } y ^ { 2 } + 81,648 x ^ { 6 } y ^ { 3 }$
B) $6561 x ^ { 8 } + 34,992 x ^ { 7 } y + 81,648 x ^ { 6 } y ^ { 2 }$
C) $8 x ^ { 8 } y + 7 x ^ { 7 } y ^ { 2 } + 6 x ^ { 6 } y ^ { 3 }$
D) $8 x ^ { 8 } + 7 x ^ { 7 } y + 6 x ^ { 6 } y ^ { 2 }$

Question

Quizplus · Accepted Answer

The correct expansion uses the binomial theorem, where the coefficients are determined by the binomial coefficients $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ for the term $x^{n-k}y^k$ in the expansion of $(x+y)^n$. For $(3x + 2y)^8$, the first three terms are calculated as follows: - The first term is $\binom{8}{0}(3x)^8(2y)^0 = 6561x^8$. - The second term is $\binom{8}{1}(3x)^7(2y)^1 = 34,992x^7y$. - The third term is $\binom{8}{2}(3x)^6(2y)^2 = 81,648x^6y^2$.

Write the First Three Terms of the Expansion (3x+2y)8( 3 x + 2 y ) ^ { 8 }(3x+2y)8

Write the First Three Terms of the Expansion $( 3 x + 2 y ) ^ { 8 }$