Question

My question?

Answer 1

replace X with (A + H)

Answer 2

yes but

Answer 3

where do the numbers go?

Answer 4

\[f(x) = 2x^3\]
\[f(a+h)=2(a+h)^3\]
So what you have to do here is expand \((a+h)^3\) and then multiply that by 2. Do you know how to do this?

Answer 5

sadly no.. can you show me?

Answer 6

Do you know how to expand \((a+h)^2\) ? (That's easier than taking it to the third power.)

Answer 7

a^2 + h^2

Answer 8

Not quite. This is expanding the product of binomials.

Here's one way to do it using the distributive property.
\[
\begin{align}
(a+h)^2 & = (a+h)(a+h)\\
& = a(a+h) + h(a+h) \\
& = a^2 + ah + ha + h^2 \\
& = a^2 + ah + ah + h^2 \\
& = a^2 + 2ah + h^2
\end{align}
\]
That might seem like a bit much so I attached a picture which shows some other ways. Here is a nice webpage which has some more examples. http://www.regentsprep.org/regents/math/algebra/AV3/Smul_bin.htm

Basically you have to know how to expand (something)^2 before you can expand (something)^3. :)