Find the coefficient a of the term in the expansion of the binomial. Binomial Terms
$( 2 x - 5 y ) ^ { 9 } ~a x ^ { 4 } y ^ { 5 }$
A)-6,300,001
B)-6,300,002
C)-6,299,999
D)-6,300,000
E)-6,299,997

Question

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms
$( 2 x - 5 y ) ^ { 9 } ~a x ^ { 4 } y ^ { 5 }$ ​
A)-6,300,001
B)-6,300,002
C)-6,299,999
D)-6,300,000
E)-6,299,997

Quizplus · Accepted Answer

The coefficient in the term is given by the formula:

Coefficient = (n choose k) * a^(n-k) * b^k

In this case, n=20, k=7, and b=-3. The coefficient involves (20 choose 7), which is 77520. Therefore, we have:

a^(13) * (-3)^7 * 77520

Simplifying this, we get:

a^(13) * (-2187) * 77520

= -16918672480 * a^13

Therefore, the coefficient is -6,300,000, which is answer choice (D).

Find the Coefficient a of the Term in the Expansion (2x−5y)9 ax4y5( 2 x - 5 y ) ^ { 9 } ~a x ^ { 4 } y ^ { 5 }(2x−5y)9 ax4y5

Find the Coefficient a of the Term in the Expansion $( 2 x - 5 y ) ^ { 9 } ~a x ^ { 4 } y ^ { 5 }$