Finite Math Examples

${(25 \sqrt{3} - 25 - 5 \sqrt{3} - 25)}^{2}$

Step 1

Simplify by adding terms.

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Step 1.1

Subtract $5 \sqrt{3}$ from $25 \sqrt{3}$ .

${(- 25 + 20 \sqrt{3} - 25)}^{2}$

Step 1.2

Simplify the expression.

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Step 1.2.1

Subtract $25$ from $- 25$ .

${(- 50 + 20 \sqrt{3})}^{2}$

Step 1.2.2

Rewrite ${(- 50 + 20 \sqrt{3})}^{2}$ as $(- 50 + 20 \sqrt{3}) (- 50 + 20 \sqrt{3})$ .

$(- 50 + 20 \sqrt{3}) (- 50 + 20 \sqrt{3})$

Step 2

Expand $(- 50 + 20 \sqrt{3}) (- 50 + 20 \sqrt{3})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- 50 (- 50 + 20 \sqrt{3}) + 20 \sqrt{3} (- 50 + 20 \sqrt{3})$

Step 2.2

Apply the distributive property.

$- 50 \cdot - 50 - 50 (20 \sqrt{3}) + 20 \sqrt{3} (- 50 + 20 \sqrt{3})$

Step 2.3

Apply the distributive property.

$- 50 \cdot - 50 - 50 (20 \sqrt{3}) + 20 \sqrt{3} \cdot - 50 + 20 \sqrt{3} (20 \sqrt{3})$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $- 50$ by $- 50$ .

$2500 - 50 (20 \sqrt{3}) + 20 \sqrt{3} \cdot - 50 + 20 \sqrt{3} (20 \sqrt{3})$

Step 3.1.2

Multiply $20$ by $- 50$ .

$2500 - 1000 \sqrt{3} + 20 \sqrt{3} \cdot - 50 + 20 \sqrt{3} (20 \sqrt{3})$

Step 3.1.3

Multiply $- 50$ by $20$ .

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 20 \sqrt{3} (20 \sqrt{3})$

Step 3.1.4

Multiply $20 \sqrt{3} (20 \sqrt{3})$ .

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Step 3.1.4.1

Multiply $20$ by $20$ .

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 \sqrt{3} \sqrt{3}$

Step 3.1.4.2

Raise $\sqrt{3}$ to the power of $1$ .

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 ({\sqrt{3}}^{1} \sqrt{3})$

Step 3.1.4.3

Raise $\sqrt{3}$ to the power of $1$ .

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 3.1.4.4

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

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 {\sqrt{3}}^{1 + 1}$

Step 3.1.4.5

Add $1$ and $1$ .

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 {\sqrt{3}}^{2}$

Step 3.1.5

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 3.1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 {(3^{\frac{1}{2}})}^{2}$

Step 3.1.5.2

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

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 3.1.5.3

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

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 \cdot 3^{\frac{2}{2}}$

Step 3.1.5.4

Cancel the common factor of $2$ .

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Step 3.1.5.4.1

Cancel the common factor.

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 \cdot 3^{\frac{2}{2}}$

Step 3.1.5.4.2

Rewrite the expression.

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 \cdot 3^{1}$

Step 3.1.5.5

Evaluate the exponent.

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 400 \cdot 3$

Step 3.1.6

Multiply $400$ by $3$ .

$2500 - 1000 \sqrt{3} - 1000 \sqrt{3} + 1200$

Step 3.2

Add $2500$ and $1200$ .

$3700 - 1000 \sqrt{3} - 1000 \sqrt{3}$

Step 3.3

Subtract $1000 \sqrt{3}$ from $- 1000 \sqrt{3}$ .

$3700 - 2000 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3700 - 2000 \sqrt{3}$

Decimal Form:

$235.89838486 \dots$