Determine g (x+a) - g (x) for the following function.

g (x) = 4x2-6x

8ax + (4a² - 6a)

Step-by-step explanation:

g (x) = 4x²-6x

g (x+a)

= 4 (x+a) ² - 6 (x+a)

= 4 (x² + 2ax + a²) - 6x - 6a

= 4x² + (4) 2ax + (4) a² - 6x - 6a

= 4x² + 8ax + 4a² - 6x - 6a

= 4x² + 8ax - 6x + 4a² - 6a

= 4x² + (8a - 6) x + (4a² - 6a)

g (x+a) - g (x)

= [4x² + (8a - 6) x + (4a² - 6a) ] - (4x²-6x)

= 4x² + (8a - 6) x + (4a² - 6a) - 4x² + 6x

= (8a - 6) x + (4a² - 6a) + 6x

= (8a - 6 + 6) x + (4a² - 6a)

= 8ax + (4a² - 6a)