Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( 2 x - 5 y ) ^ { 8 }$ $a x ^ { 3 } y ^ { 5 }$
A) $a = - 224000$
B) $a = 336$
C) $a = 40$
D) $a = 8$
E) $a = 390,625$

Question

Quizplus · Accepted Answer

The coefficient of $x^3y^5$ in the expansion of $(2x-5y)^8$ can be found using the binomial theorem, specifically the term is given by $\binom{8}{3}(2x)^3(-5y)^5$. Calculating this gives $\binom{8}{3} \cdot 2^3 \cdot (-5)^5 = 56 \cdot 8 \cdot -3125 = -224000$.

Find the Coefficient a of the Term in the Expansion (2x−5y)8( 2 x - 5 y ) ^ { 8 }(2x−5y)8

Find the Coefficient a of the Term in the Expansion $( 2 x - 5 y ) ^ { 8 }$