Answer:
[tex]f(x+h)=x^2+2xh+h^2+2x+2h[/tex]
Option D is correct option.
Step-by-step explanation:
We are given: [tex]f(x)=x^2+2x[/tex]
We need to find f(x+h)
For finding f(x+h) we need to replace x by x+h
[tex]f(x+h)=(x+h)^2+2(x+h)\\We \ know \ (a+b)^2=a^2+2ab+b^2\\f(x+h)=x^2+2xh+h^2+2x+2h[/tex]
Finding f(x+h) we get:
[tex]f(x+h)=x^2+2xh+h^2+2x+2h[/tex]
Option D is correct option.
