Question

what is the coefficient of x^3y^2 in the expansion of (2x + y)^5? If there isn't one state "It does not exist"
a. 2
b. 5
c. 40
d. 80
e. It does not exist

Answer 1

sure it exists, since \(2+3=5\) i.e. the exponents add to 5

Answer 2

compute it as \(\binom{5}{2}(2x)^3y^2\) where \(\binom{5}{2}=\frac{5\times 4}{2}=10\) and so \(10(2x)^3y^2=10\times 8x^3y^2=80x^3y^2\)

Answer 3

I got it now thanks