Question

How can i find the coefficients of the function f(x+a) if i know f(x):
For example: f(x)=x^3+6x^2+4x+8
find f(x+a)

Answer 1

f(x)=x^3+6x^2+4x+8
f(x+a)=(x+a)^3+6(x+a)^2+4(x+a)+8 = ... ?

Answer 2

Yes , but i want the coefficients after expanding

Answer 3

so, expand

Answer 4

there is a method for direct finding the coefficients not expanding manually. but i don't remember this method

Answer 5

A similar but also lazier way is to look for the coefficient with the same power of x, say for x^2, I have 3ax^2 and 6x^2, hence the coefficient will be 3a+6