Find the coefficient a of the term in the expansion of the binomial. Binomial Terms
$( x - 7 y ) ^ { 10 } ~a x ^ { 8 } y ^ { 2 }$
A)2,208
B)2,204
C)2,206
D)2,205
E)2,203

Question

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms
$( x - 7 y ) ^ { 10 } ~a x ^ { 8 } y ^ { 2 }$ ​
A)2,208
B)2,204
C)2,206
D)2,205
E)2,203

Quizplus · Accepted Answer

The coefficient of the term in the expansion of the binomial can be found using the binomial theorem. The general term of the expansion is given by:

$$ \binom{10}{k} x^{10-k} (-7y)^k = \binom{10}{k} (-1)^k 7^k x^{10-k} y^k $$

To obtain a term of the form $ax^8 y^2$, we need $k$ to satisfy $10-k+2k=8$, or $k=2$. Therefore, the coefficient of $ax^8 y^2$ is given by:

$$ (-1)^2 \binom{10}{2} 7^2 = 2,205$$

Therefore, the answer is D) 2,205.

Find the Coefficient a of the Term in the Expansion (x−7y)10 ax8y2( x - 7 y ) ^ { 10 } ~a x ^ { 8 } y ^ { 2 }(x−7y)10 ax8y2

Find the Coefficient a of the Term in the Expansion $( x - 7 y ) ^ { 10 } ~a x ^ { 8 } y ^ { 2 }$