The coefficient of x^2 in the expansion of (2x^2 + 1 x )¹⁰ , x 0 , is :

Step-by-step solution

The general term in the expansion of (2x^2 + 1 x )¹⁰ is given by: T_ r+1 = ¹⁰C_ r (2x^2)^ 10-r ( 1 x )^r T_ r+1 = ¹⁰C_ r 2^ 10-r x^ 20-2r x^ -r T_ r+1 = ¹⁰C_ r 2^ 10-r x^ 20-3r For the coefficient of x^2 , we equate the power of x to 2 : 20 - 3r = 2 3r = 18 r = 6 Substituting r = 6 in the coefficient part, we get: Coefficient = ¹⁰C₆ 2¹⁰⁻⁶ = ¹⁰C₄ 2^4 = 10 9 8 7 4 3 2 1 16 = 210 16 = 3360 Answer: 3360