Question

Multiply? I don't know how to do this o.o

(X+4√2) (x-4√2) (x-3i)

Answer 1

`x^(3) -(3i) \; x^(2) -32x + 96 i`.

Explanation:

Notice that the first two factors are in the form
`(x-a)(x+a)`, which is equal to
`(x^(2) - a^(2))`. Start by combining and expanding these two factors:

Let
`a = 4√(2)`.

`a^(2) = 16 * 2 = 32`.

`(x + a) (x - a) = x^(2) - a^(2) = x^(2) -32`.

This expression can now be expressed as
`(x^(2) - 32)(x - 3i)`.
`i` stands the unit imaginary number, where
`i^(2) = -1`. Unless
`i` is raised to a certain power other than
`1`, it can be treated just like a constant.

Expand this expression using FOIL:

`\begin{aligned}&(x^(2) - 32)(x - 3i)\\=&\underbrace{x^(2)\cdot x}_(\verb!F!) +\underbrace{(x^(2))(-3i)}_(\verb!O!) + \underbrace{(-32)x}_(\verb!I!) + \underbrace{(-32)(-3i)}_(\verb!L!)\\=& x^(3) -(3i)x^(2)-32x + 96i \end{aligned}`.