Question

How do you find the coefficient of `x^2` in the expansion of `(2+x)^5`?

Answer 1

80

Explanation:

Binomial coefficient are may be found by applyıng the Pascal's rule . Pascal's rule or the Pascal's triangle can easiliy be found in the internet. `(x+y)^5=x^5 +5x^4y+ 10x^3y^2+10x^2y^3+5xy^4+y^5`
the x in the question correspond to y in the formulation. Acoording to this `(2+x)^5=2^5 +5.2^4x+ 10.2^3x^2+10.2^2x^3+5.2x^4+x^5`
or `(2+x)^5=32 +80x+ 80x^2+40x^3+10x^4+x^5` Therefore the coefficient of `x^2` in the expansion of `(2+x)^5` is 80.