Basic Math Examples

$(1 - \sqrt{2} - 1) (2 + \sqrt{2} \cdot 4)$

Step 1

Simplify by subtracting numbers.

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Step 1.1

Subtract $1$ from $1$ .

$(0 - \sqrt{2}) (2 + \sqrt{2} \cdot 4)$

Step 1.2

Subtract $\sqrt{2}$ from $0$ .

$- \sqrt{2} (2 + \sqrt{2} \cdot 4)$

Step 2

Move $4$ to the left of $\sqrt{2}$ .

$- \sqrt{2} (2 + 4 \sqrt{2})$

Step 3

Simplify by multiplying through.

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Step 3.1

Apply the distributive property.

$- \sqrt{2} \cdot 2 - \sqrt{2} (4 \sqrt{2})$

Step 3.2

Multiply $2$ by $- 1$ .

$- 2 \sqrt{2} - \sqrt{2} (4 \sqrt{2})$

Step 4

Multiply $- \sqrt{2} (4 \sqrt{2})$ .

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Step 4.1

Multiply $4$ by $- 1$ .

$- 2 \sqrt{2} - 4 \sqrt{2} \sqrt{2}$

Step 4.2

Raise $\sqrt{2}$ to the power of $1$ .

$- 2 \sqrt{2} - 4 ({\sqrt{2}}^{1} \sqrt{2})$

Step 4.3

Raise $\sqrt{2}$ to the power of $1$ .

$- 2 \sqrt{2} - 4 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 4.4

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

$- 2 \sqrt{2} - 4 {\sqrt{2}}^{1 + 1}$

Step 4.5

Add $1$ and $1$ .

$- 2 \sqrt{2} - 4 {\sqrt{2}}^{2}$

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

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

$- 2 \sqrt{2} - 4 {(2^{\frac{1}{2}})}^{2}$

Step 5.1.2

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

$- 2 \sqrt{2} - 4 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 5.1.3

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

$- 2 \sqrt{2} - 4 \cdot 2^{\frac{2}{2}}$

Step 5.1.4

Cancel the common factor of $2$ .

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Step 5.1.4.1

Cancel the common factor.

$- 2 \sqrt{2} - 4 \cdot 2^{\frac{2}{2}}$

Step 5.1.4.2

Rewrite the expression.

$- 2 \sqrt{2} - 4 \cdot 2^{1}$

Step 5.1.5

Evaluate the exponent.

$- 2 \sqrt{2} - 4 \cdot 2$

Step 5.2

Multiply $- 4$ by $2$ .

$- 2 \sqrt{2} - 8$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{2} - 8$

Decimal Form:

$- 10.82842712 \dots$