Simplify 6xi^3(-4xi+5)

$6 x i^{3} (- 4 x i + 5)$

Step 1

Factor out $i^{2}$ .

$6 x (i^{2} \cdot i) (- 4 x i + 5)$

Step 2

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

$6 x (- 1 \cdot i) (- 4 x i + 5)$

Step 3

Simplify the expression.

Rewrite $- 1 i$ as $- i$ .

$6 x (- i) (- 4 x i + 5)$

Multiply $- 1$ by $6$ .

$- 6 x i (- 4 x i + 5)$

$- 6 x i (- 4 x i + 5)$

Step 4

Apply the distributive property.

$- 6 x i (- 4 x i) - 6 x i \cdot 5$

Step 5

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 6 (x \cdot x) i (- 4 i) - 6 x i \cdot 5$

Multiply $x$ by $x$ .

$- 6 x^{2} i (- 4 i) - 6 x i \cdot 5$

$- 6 x^{2} i (- 4 i) - 6 x i \cdot 5$

Step 6

Multiply $5$ by $- 6$ .

$- 6 x^{2} i (- 4 i) - 30 x i$

Step 7

Simplify each term.

Multiply $- 6 x^{2} i (- 4 i)$ .

Multiply $- 4$ by $- 6$ .

$24 x^{2} i i - 30 x i$

Raise $i$ to the power of $1$ .

$24 x^{2} (i^{1} i) - 30 x i$

Raise $i$ to the power of $1$ .

$24 x^{2} (i^{1} i^{1}) - 30 x i$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$24 x^{2} i^{1 + 1} - 30 x i$

Add $1$ and $1$ .

$24 x^{2} i^{2} - 30 x i$

$24 x^{2} i^{2} - 30 x i$

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

$24 x^{2} \cdot - 1 - 30 x i$

Multiply $- 1$ by $24$ .

$- 24 x^{2} - 30 x i$

$- 24 x^{2} - 30 x i$

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