Polynomial multiplication with complex numbers

Question

I'm looking for the step-by-step for how to multiply the following problem on Khan Academy, because I'm getting a different answer.

$$x(x+3i)(x-2i)$$

I tried distributing the $x$ over both expressions and then multiplied the two expressions together for the result:$$ x^4 -2x^3i + 3x^3i - 6x^2i^2 \implies x^4 - x^3i + 6x^2$$

How should I do?

Answer 1

Distributing the monomial $x$ last makes work much, much easier.

\begin{align} x(x+3i)(x-2i)&=x(x^2+ix-6i^2)\\ &=x(x^2+ix+6)\\ &=x^3+ix^2+6x \end{align}

Answer 2

$x(x+3i)(x-2i)$

$(x^2+3xi)(x-2i)$

$x^3-2x^2i+3x^2i-6xi^2$

$x^3+x^2i+6x$