Question

(x + 2) is raised to the fifth power. What is the correct expansion for C(5,3)?

C(5,3) x2³
C(5,3) x²2³
C(5,3) x³2²

Answer 1

Formula. Binomial theorem:

`(x + y)^ n = C(n,0) x^(ny)^(0) + C(n,1)x^((n-1)) \ \ y + C(n,2)x^((n-2)) \ y^2 + ...+ C(n,n+1)xy^((n-1)) + C(n,n)x^(0y)^n`

So, for n = 5:

`(x + 2)^5 = C(5,0)x^5 + C(5,1)x^4 \ . \ 2 + C(5,2) x^3 \ . \ 2^2 + C(5,3)x^2 \ . \ 2^3 + C(5,4)x \ . \ 2^4 + C(5,5) \ . \ 2^5`

So, the third term is
`\bold{C(5,2)x^3 2^2}`