Write in Standard Form (-1- square root of -6)^2

${(- 1 - \sqrt{- 6})}^{2}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify terms.

Simplify each term.

Rewrite $- 6$ as $- 1 (6)$ .

${(- 1 - \sqrt{- 1 (6)})}^{2}$

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

${(- 1 - (\sqrt{- 1} \cdot \sqrt{6}))}^{2}$

Rewrite $\sqrt{- 1}$ as $i$ .

${(- 1 - i \sqrt{6})}^{2}$

Rewrite ${(- 1 - i \sqrt{6})}^{2}$ as $(- 1 - i \sqrt{6}) (- 1 - i \sqrt{6})$ .

$(- 1 - i \sqrt{6}) (- 1 - i \sqrt{6})$

Step 3

Expand $(- 1 - i \sqrt{6}) (- 1 - i \sqrt{6})$ using the FOIL Method.

Apply the distributive property.

$- 1 (- 1 - i \sqrt{6}) - i \sqrt{6} (- 1 - i \sqrt{6})$

Apply the distributive property.

$- 1 \cdot - 1 - 1 (- i \sqrt{6}) - i \sqrt{6} (- 1 - i \sqrt{6})$

Apply the distributive property.

$- 1 \cdot - 1 - 1 (- i \sqrt{6}) - i \sqrt{6} \cdot - 1 - i \sqrt{6} (- i \sqrt{6})$

Step 4

Simplify and combine like terms.

Simplify each term.

Multiply $- 1$ by $- 1$ .

$1 - 1 (- i \sqrt{6}) - i \sqrt{6} \cdot - 1 - i \sqrt{6} (- i \sqrt{6})$

Multiply $- 1 (- i \sqrt{6})$ .

Multiply $- 1$ by $- 1$ .

$1 + 1 (i \sqrt{6}) - i \sqrt{6} \cdot - 1 - i \sqrt{6} (- i \sqrt{6})$

Multiply $\sqrt{6}$ by $1$ .

$1 + \sqrt{6} i - i \sqrt{6} \cdot - 1 - i \sqrt{6} (- i \sqrt{6})$

Multiply $- i \sqrt{6} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$1 + \sqrt{6} i + 1 i \sqrt{6} - i \sqrt{6} (- i \sqrt{6})$

Multiply $\sqrt{6}$ by $1$ .

$1 + \sqrt{6} i + \sqrt{6} i - i \sqrt{6} (- i \sqrt{6})$

Multiply $- i \sqrt{6} (- i \sqrt{6})$ .

Multiply $- 1$ by $- 1$ .

$1 + \sqrt{6} i + \sqrt{6} i + 1 i \sqrt{6} (i \sqrt{6})$

Multiply $\sqrt{6}$ by $1$ .

$1 + \sqrt{6} i + \sqrt{6} i + \sqrt{6} i (i \sqrt{6})$

Raise $\sqrt{6}$ to the power of $1$ .

$1 + \sqrt{6} i + \sqrt{6} i + {\sqrt{6}}^{1} \sqrt{6} i i$

Raise $\sqrt{6}$ to the power of $1$ .

$1 + \sqrt{6} i + \sqrt{6} i + {\sqrt{6}}^{1} {\sqrt{6}}^{1} i i$

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

$1 + \sqrt{6} i + \sqrt{6} i + {\sqrt{6}}^{1 + 1} i i$

Add $1$ and $1$ .

$1 + \sqrt{6} i + \sqrt{6} i + {\sqrt{6}}^{2} i i$

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

$1 + \sqrt{6} i + \sqrt{6} i + {\sqrt{6}}^{2} (i^{1} i)$

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

$1 + \sqrt{6} i + \sqrt{6} i + {\sqrt{6}}^{2} (i^{1} i^{1})$

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

$1 + \sqrt{6} i + \sqrt{6} i + {\sqrt{6}}^{2} i^{1 + 1}$

Add $1$ and $1$ .

$1 + \sqrt{6} i + \sqrt{6} i + {\sqrt{6}}^{2} i^{2}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$1 + \sqrt{6} i + \sqrt{6} i + {(6^{\frac{1}{2}})}^{2} i^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$1 + \sqrt{6} i + \sqrt{6} i + 6^{\frac{1}{2} \cdot 2} i^{2}$

Combine $\frac{1}{2}$ and $2$ .

$1 + \sqrt{6} i + \sqrt{6} i + 6^{\frac{2}{2}} i^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$1 + \sqrt{6} i + \sqrt{6} i + 6^{\frac{2}{2}} i^{2}$

Rewrite the expression.

$1 + \sqrt{6} i + \sqrt{6} i + 6^{1} i^{2}$

Evaluate the exponent.

$1 + \sqrt{6} i + \sqrt{6} i + 6 i^{2}$

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

$1 + \sqrt{6} i + \sqrt{6} i + 6 \cdot - 1$

Multiply $6$ by $- 1$ .

$1 + \sqrt{6} i + \sqrt{6} i - 6$

Subtract $6$ from $1$ .

$- 5 + \sqrt{6} i + \sqrt{6} i$

Add $\sqrt{6} i$ and $\sqrt{6} i$ .

$- 5 + 2 \sqrt{6} i$

Write in Standard Form (-1- square root of -6)^2

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