determine g(x+a)-g(x) for g(x)=5x^2-x

Question

determine g(x+a)-g(x) for g(x)=5x^2-x

Answer 1

g([ ]) = 5[ ]² - [ ]

So g (x + a) = 5[x + a]² - [x + a] = 5[x² + 2ax +a²] - x - a = 5x² + 10ax + 5a² - x - a

g(x) = 5x² - x

So, g(x + a) - g(x) = 5x² +10ax + 5a² - x - a - [5x² - x] = 10ax + 5a² - a

This could also be written as:

a ( 10x + 5a - 1)