Simplify 6-(3x-2i)^2

$6 - {(3 x - 2 i)}^{2}$

Simplify each term.

Rewrite ${(3 x - 2 i)}^{2}$ as $(3 x - 2 i) (3 x - 2 i)$ .

$6 - ((3 x - 2 i) (3 x - 2 i))$

Expand $(3 x - 2 i) (3 x - 2 i)$ using the FOIL Method.

Apply the distributive property.

$6 - (3 x (3 x - 2 i) - 2 i (3 x - 2 i))$

Apply the distributive property.

$6 - (3 x (3 x) + 3 x (- 2 i) - 2 i (3 x - 2 i))$

Apply the distributive property.

$6 - (3 x (3 x) + 3 x (- 2 i) - 2 i (3 x) - 2 i (- 2 i))$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$6 - (3 \cdot 3 x \cdot x + 3 x (- 2 i) - 2 i (3 x) - 2 i (- 2 i))$

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

Move $x$ .

$6 - (3 \cdot 3 (x \cdot x) + 3 x (- 2 i) - 2 i (3 x) - 2 i (- 2 i))$

Multiply $x$ by $x$ .

$6 - (3 \cdot 3 x^{2} + 3 x (- 2 i) - 2 i (3 x) - 2 i (- 2 i))$

Multiply $3$ by $3$ .

$6 - (9 x^{2} + 3 x (- 2 i) - 2 i (3 x) - 2 i (- 2 i))$

Multiply $- 2$ by $3$ .

$6 - (9 x^{2} - 6 x i - 2 i (3 x) - 2 i (- 2 i))$

Multiply $3$ by $- 2$ .

$6 - (9 x^{2} - 6 x i - 6 i x - 2 i (- 2 i))$

Multiply $- 2 i (- 2 i)$ .

Multiply $- 2$ by $- 2$ .

$6 - (9 x^{2} - 6 x i - 6 i x + 4 i i)$

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

$6 - (9 x^{2} - 6 x i - 6 i x + 4 (i^{1} i))$

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

$6 - (9 x^{2} - 6 x i - 6 i x + 4 (i^{1} i^{1}))$

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

$6 - (9 x^{2} - 6 x i - 6 i x + 4 i^{1 + 1})$

Add $1$ and $1$ .

$6 - (9 x^{2} - 6 x i - 6 i x + 4 i^{2})$

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

$6 - (9 x^{2} - 6 x i - 6 i x + 4 \cdot - 1)$

Multiply $4$ by $- 1$ .

$6 - (9 x^{2} - 6 x i - 6 i x - 4)$

Subtract $6 i x$ from $- 6 x i$ .

Move $i$ .

$6 - (9 x^{2} - 6 x i - 6 x i - 4)$

Subtract $6 x i$ from $- 6 x i$ .

$6 - (9 x^{2} - 12 x i - 4)$

Apply the distributive property.

$6 - (9 x^{2}) - (- 12 x i) - - 4$

Simplify.

Multiply $9$ by $- 1$ .

$6 - 9 x^{2} - (- 12 x i) - - 4$

Multiply $- 12$ by $- 1$ .

$6 - 9 x^{2} + 12 (x i) - - 4$

Multiply $- 1$ by $- 4$ .

$6 - 9 x^{2} + 12 (x i) + 4$

$6 - 9 x^{2} + 12 x i + 4$

Add $6$ and $4$ .

$- 9 x^{2} + 12 x i + 10$

Simplify 6-(3x-2i)^2

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