Question

Can someone please help me with this math problem, ASAP? It is in the picture, Thanks!

Answer 1

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

So,
`g(x+a) = 4(x+a)^2 + 3(x+a)`, since we're just substituting (x+a) for x.

If we clean that up a bit,

`\begin{aligned}g(x+a) &= 4(x+a)^2 + 3(x+a)\\[0.5em] &= 4(x^2+2xa+a^2) + 3x+3a\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a\end{aligned}`

Now putting this all together:

`\begin{aligned}g(x+a)-g(x) &= ( 4x^2+8xa+4a^2 + 3x+3a) - (4x^2+3x)\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a - 4x^2-3x\\[0.5em]&= 8xa+4a^2 +3a\end{aligned}`

Remember that
`(x+a)^2 = (x+a)(x+a) = x^2+2xa+a^2`