Write in Standard Form (-3- square root of -7)^2

${(- 3 - \sqrt{- 7})}^{2}$

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

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

Simplify terms.

Simplify each term.

Rewrite $- 7$ as $- 1 (7)$ .

${(- 3 - \sqrt{- 1 (7)})}^{2}$

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

${(- 3 - (\sqrt{- 1} \cdot \sqrt{7}))}^{2}$

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

${(- 3 - i \sqrt{7})}^{2}$

Rewrite ${(- 3 - i \sqrt{7})}^{2}$ as $(- 3 - i \sqrt{7}) (- 3 - i \sqrt{7})$ .

$(- 3 - i \sqrt{7}) (- 3 - i \sqrt{7})$

Expand $(- 3 - i \sqrt{7}) (- 3 - i \sqrt{7})$ using the FOIL Method.

Apply the distributive property.

$- 3 (- 3 - i \sqrt{7}) - i \sqrt{7} (- 3 - i \sqrt{7})$

Apply the distributive property.

$- 3 \cdot - 3 - 3 (- i \sqrt{7}) - i \sqrt{7} (- 3 - i \sqrt{7})$

Apply the distributive property.

$- 3 \cdot - 3 - 3 (- i \sqrt{7}) - i \sqrt{7} \cdot - 3 - i \sqrt{7} (- i \sqrt{7})$

Simplify and combine like terms.

Simplify each term.

Multiply $- 3$ by $- 3$ .

$9 - 3 (- i \sqrt{7}) - i \sqrt{7} \cdot - 3 - i \sqrt{7} (- i \sqrt{7})$

Multiply $- 1$ by $- 3$ .

$9 + 3 (i \sqrt{7}) - i \sqrt{7} \cdot - 3 - i \sqrt{7} (- i \sqrt{7})$

Multiply $- 3$ by $- 1$ .

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} - i \sqrt{7} (- i \sqrt{7})$

Multiply $- i \sqrt{7} (- i \sqrt{7})$ .

Multiply $- 1$ by $- 1$ .

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + 1 i \sqrt{7} (i \sqrt{7})$

Multiply $\sqrt{7}$ by $1$ .

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + \sqrt{7} i (i \sqrt{7})$

Raise $\sqrt{7}$ to the power of $1$ .

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + {\sqrt{7}}^{1} \sqrt{7} i i$

Raise $\sqrt{7}$ to the power of $1$ .

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + {\sqrt{7}}^{1} {\sqrt{7}}^{1} i i$

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

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + {\sqrt{7}}^{1 + 1} i i$

Add $1$ and $1$ .

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + {\sqrt{7}}^{2} i i$

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

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + {\sqrt{7}}^{2} (i^{1} i)$

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

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + {\sqrt{7}}^{2} (i^{1} i^{1})$

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

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + {\sqrt{7}}^{2} i^{1 + 1}$

Add $1$ and $1$ .

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + {\sqrt{7}}^{2} i^{2}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + {(7^{\frac{1}{2}})}^{2} i^{2}$

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

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + 7^{\frac{1}{2} \cdot 2} i^{2}$

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

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + 7^{\frac{2}{2}} i^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + 7^{\frac{2}{2}} i^{2}$

Rewrite the expression.

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + 7^{1} i^{2}$

Evaluate the exponent.

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + 7 i^{2}$

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

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} + 7 \cdot - 1$

Multiply $7$ by $- 1$ .

$9 + 3 i \sqrt{7} + 3 i \sqrt{7} - 7$

Subtract $7$ from $9$ .

$3 i \sqrt{7} + 3 i \sqrt{7} + 2$

Add $3 i \sqrt{7}$ and $3 i \sqrt{7}$ .

$6 i \sqrt{7} + 2$

Reorder $6 i \sqrt{7}$ and $2$ .

$2 + 6 i \sqrt{7}$

Write in Standard Form (-3- square root of -7)^2

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