Simplify x(3i^2)^3+2xi^12

$x {(3 i^{2})}^{3} + 2 x i^{12}$

Step 1

Simplify each term.

Rewrite $i^{2}$ as $- 1$ .

$x {(3 \cdot - 1)}^{3} + 2 x i^{12}$

Multiply $3$ by $- 1$ .

$x {(- 3)}^{3} + 2 x i^{12}$

Raise $- 3$ to the power of $3$ .

$x \cdot - 27 + 2 x i^{12}$

Move $- 27$ to the left of $x$ .

$- 27 \cdot x + 2 x i^{12}$

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

$- 27 x + 2 x {(i^{4})}^{3}$

Rewrite $i^{4}$ as $1$ .

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 27 x + 2 x {({(i^{2})}^{2})}^{3}$

Rewrite $i^{2}$ as $- 1$ .

$- 27 x + 2 x {({(- 1)}^{2})}^{3}$

Raise $- 1$ to the power of $2$ .

$- 27 x + 2 x \cdot 1^{3}$

$- 27 x + 2 x \cdot 1^{3}$

One to any power is one.

$- 27 x + 2 x \cdot 1$

Multiply $2$ by $1$ .

$- 27 x + 2 x$

$- 27 x + 2 x$

Step 2

Add $- 27 x$ and $2 x$ .

$- 25 x$

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