Question

Multiply? I don't know how to do this o.o (X+4√2) (x-4√2) (x-3i)

Answer 1

Answer:

$x^{3} -(3i) \; x^{2} -32x + 96 i$.

Step-by-step 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 $a = 4\sqrt{2}$.

$a^{2} = 16 \times 2 = 32$.

$(x + a) (x - a) = x^{2} - a^{2} = x^{2} -32$.

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:

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