Can you include a stepbystep of the entire binomial expansio

Can you include a step-by-step of the entire binomial expansion including terms that equal 1?

The third term in the expansion of (x + k)^8 is 63 x^6. Find the possible values of k.

Solution

(x+k)⁸

(x+k)⁸=⁸c₀x⁸k⁰ +⁸c₁x⁷k +⁸c₂x⁶k²+⁸c₃x⁵k³+⁸c₄x⁴k⁴+⁸c₅x³k⁵+⁸c₆x²k⁶+⁸c₇xk⁷+⁸c₈x⁰k⁸

(x+k)⁸= x⁸ +8x⁷k +28x⁶k²+56x⁵k³+70x⁴k⁴+56x³k⁵+28x²k⁶+8xk⁷+k⁸

third term =⁸c_3-1 x^8-(3-1) k^3-1

third term =⁸c₂ x⁶k²

third term =28x⁶k²

28x⁶k²=63x⁶

28k²=63

k²=63/28

k²=9/4

k=3/2