Find the coefficient $a$ of the term in the expansion of the binomial.
$ \begin{array}{ll}\text { Binomial } & \text { Term } \ (2 x-5 y)^{7} & a x^{2} y^{5}\end{array} $
A) $a = 12$
B) $a = - 262,500$
C) $a = 14$
D) $a = - 78,125$
E) $\quad a = 2520$

Question

Quizplus · Accepted Answer

The term $ax^2y^5$ in the expansion of $(2x-5y)^7$ can be found using the binomial theorem, which gives the coefficient as $\binom{7}{2}(2x)^2(-5y)^5 = \binom{7}{2} \cdot 4 \cdot (-3125) = 21 \cdot 4 \cdot (-3125) = -262,500$.

Find the Coefficient aaa Of the Term in the Expansion of the Binomial

Find the Coefficient $a$ Of the Term in the Expansion of the Binomial