Find the coeffcient a of the given term in the expansion of the binomial

binomial= (x-2y)^10
term= ax^8y^2

Question

Find the coeffcient a of the given term in the expansion of the binomial

binomial= (x-2y)^10
term= ax^8y^2

rational · Answer

$$\large  \binom{10}{2} x^{8}(-2y)^2$$

anonymous · Answer

ok uh how do you do this?

rational · Answer

anonymous · Answer

on the test we are not allowed to use a calculator

rational · Answer

heard of "binomial coefficient" before ?

anonymous · Answer

uh sort of but idk how to use it

anonymous · Answer

wait ok what's the formula that you used?

rational · Answer

rational · Answer

$$\large  \binom{n}{k} = \dfrac{n!}{k!(n-k)!}$$

rational · Answer

plugin $n=10$ and $k=2$

anonymous · Answer

but the answer is 45 when you do that

anonymous · Answer

the real answer is suppose to be 180 though

rational · Answer

Yep! the term is
$$\large  \binom{10}{2} x^{8}(-2y)^2$$

plugin the value of $\binom{10}{2}$ and simplify

anonymous · Answer

wait what????
plus in 45 to what???

rational · Answer

$$\large  \binom{10}{2} x^{8}(-2y)^2 = 45 x^8(-2y)^2 = ?$$

anonymous · Answer

ohhhhhhhhhhhhhhhhhh wait, I think I get it

anonymous · Answer

it's 180

anonymous · Answer

lol thanks

anonymous · Answer

took me a while

anonymous · Answer

hey imma write a testimony btw, is it ok if it's like not the best?

anonymous · Answer

like if it's a couple of words?
that ok? 
or you don't want me to write a sloppy testimony?

rational · Answer

thats sweet <3

anonymous · Answer

i guess i'll take that as a yes

anonymous · Answer

thanks btw

rational · Answer

yw :) ty for the awesome testimonial XD

sepeario · Answer

Very well explained.