# How do you find the coefficient of a of the term ax^8y^6 in the expansion of the binomial (x^2+y)^10?

Sep 21, 2017

${\left(a + b\right)}^{10} = \left(10 C 0\right) {a}^{10} {b}^{0} + \left(10 C 1\right) {a}^{9} {b}^{1} + \left(10 C 2\right) {a}^{8} {b}^{2} + \ldots$

Continuing to the 7th term we have:

$\left(10 C 6\right) {a}^{4} {b}^{6}$

With $a \implies {x}^{2} \mathmr{and} b \implies y$ we get:

$\left(10 C 6\right) {\left({x}^{2}\right)}^{4} \left({y}^{6}\right)$

i.e. $\left(10 C 6\right) {x}^{8} {y}^{6}$

so, coefficient is 10C6 = 210

:)>