first four term of (k+x)^8

Just use the Pascal's Triangle. 

The first four terms of (k=x)^8 is:

k^8 + 8k^7 x + 28k^6 x^2 + 56k^5x^3

 

But the over-all answer is:

 k^8 + 8k^7 x + 28k^6 x^2 + 56k^5x^3 + 75k^4x^4 +56k^3x^5 +28k^2x^6 +8kx^7 +x^8