Question

(x + 2) is raised to the fifth power. The third term of the expansion is:

C(5, 3)x³2²
C(5, 3)x²2³
C(5, 2)x³2²

Answer 1

the third answer

Explanation:

Answer 2

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 C(5,2)x^3. 2^2