Find a Particular Term in a Binomial Expansion
-$$( 2 x + 3 y ) ^ { 8 }$$
A) $256 x ^ { 8 } + 3072 x ^ { 7 } y + 16,128 x ^ { 6 } y ^ { 2 }$
B) $8 x ^ { 8 } + 7 x ^ { 7 } y + 6 x ^ { 6 } y ^ { 2 }$
C) $256 x ^ { 8 } y + 3072 x ^ { 7 } y ^ { 2 } + 16,128 x ^ { 6 } y ^ { 3 }$
D) $8 x ^ { 8 } y + 7 x ^ { 7 } y ^ { 2 } + 6 x ^ { 6 } y ^ { 3 }$

Question

Quizplus · Accepted Answer

The correct term can be found using the binomial theorem, which for a term $t_{r+1}$ in the expansion of $(a + b)^n$ is given by $\binom{n}{r} a^{n-r} b^r$. The coefficients in choice A correctly follow the pattern of the binomial theorem for the expansion of $(2x + 3y)^8$, indicating it is the correct choice.

Find a Particular Term in a Binomial Expansion - (2x+3y)8( 2 x + 3 y ) ^ { 8 }(2x+3y)8

Find a Particular Term in a Binomial Expansion
- $( 2 x + 3 y ) ^ { 8 }$