Basic Math Examples

${(9 - 6 i)}^{2} - 27$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite ${(9 - 6 i)}^{2}$ as $(9 - 6 i) (9 - 6 i)$ .

$(9 - 6 i) (9 - 6 i) - 27$

Step 1.2

Expand $(9 - 6 i) (9 - 6 i)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$9 (9 - 6 i) - 6 i (9 - 6 i) - 27$

Step 1.2.2

Apply the distributive property.

$9 \cdot 9 + 9 (- 6 i) - 6 i (9 - 6 i) - 27$

Step 1.2.3

Apply the distributive property.

$9 \cdot 9 + 9 (- 6 i) - 6 i \cdot 9 - 6 i (- 6 i) - 27$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $9$ by $9$ .

$81 + 9 (- 6 i) - 6 i \cdot 9 - 6 i (- 6 i) - 27$

Step 1.3.1.2

Multiply $- 6$ by $9$ .

$81 - 54 i - 6 i \cdot 9 - 6 i (- 6 i) - 27$

Step 1.3.1.3

Multiply $9$ by $- 6$ .

$81 - 54 i - 54 i - 6 i (- 6 i) - 27$

Step 1.3.1.4

Multiply $- 6 i (- 6 i)$ .

Tap for more steps...

Step 1.3.1.4.1

Multiply $- 6$ by $- 6$ .

$81 - 54 i - 54 i + 36 i i - 27$

Step 1.3.1.4.2

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

$81 - 54 i - 54 i + 36 (i^{1} i) - 27$

Step 1.3.1.4.3

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

$81 - 54 i - 54 i + 36 (i^{1} i^{1}) - 27$

Step 1.3.1.4.4

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

$81 - 54 i - 54 i + 36 i^{1 + 1} - 27$

Step 1.3.1.4.5

Add $1$ and $1$ .

$81 - 54 i - 54 i + 36 i^{2} - 27$

Step 1.3.1.5

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

$81 - 54 i - 54 i + 36 \cdot - 1 - 27$

Step 1.3.1.6

Multiply $36$ by $- 1$ .

$81 - 54 i - 54 i - 36 - 27$

Step 1.3.2

Subtract $36$ from $81$ .

$45 - 54 i - 54 i - 27$

Step 1.3.3

Subtract $54 i$ from $- 54 i$ .

$45 - 108 i - 27$

Step 2

Subtract $27$ from $45$ .

$18 - 108 i$