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

(X+4√2) (x-4√2) (x-3i)

User Daniel J F
by
8.5k points

1 Answer

4 votes

Answer:


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}.

User Lizz Parody
by
7.9k points

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