Help with College Algebra

Question

Determine g(x+a)−g(x) for the following function

g(x)=3x^2+4x

Answer 1

Plug in (x+a) into every x. Simplify, then subtract g(x).

g(x+a)=3(x+a)²+4(x+a)

=3(x+a)(x+a)+4x+4a

=3(x²+ax+ax+a²)+4x+4a

= 3(x²+2ax+a²)+4x+4a

= 3x²+6ax+3a²+4x+4a

g(x+a)-g(x)= 3x²+6ax+3a²+4x+4a-(3x²+4x)

= 3x²+6ax+3a²+4x+4a-3x²-4x

=6ax+4a+3a²

^{Hope this helps!}