Algebra Examples

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

Step 1

Rewrite ${(5 - x \sqrt{3})}^{2}$ as $(5 - x \sqrt{3}) (5 - x \sqrt{3})$ .

$(5 - x \sqrt{3}) (5 - x \sqrt{3})$

Step 2

Expand $(5 - x \sqrt{3}) (5 - x \sqrt{3})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 (5 - x \sqrt{3}) - x \sqrt{3} (5 - x \sqrt{3})$

Step 2.2

Apply the distributive property.

$5 \cdot 5 + 5 (- x \sqrt{3}) - x \sqrt{3} (5 - x \sqrt{3})$

Step 2.3

Apply the distributive property.

$5 \cdot 5 + 5 (- x \sqrt{3}) - x \sqrt{3} \cdot 5 - x \sqrt{3} (- x \sqrt{3})$

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 $5$ by $5$ .

$25 + 5 (- x \sqrt{3}) - x \sqrt{3} \cdot 5 - x \sqrt{3} (- x \sqrt{3})$

Step 3.1.2

Multiply $- 1$ by $5$ .

$25 - 5 (x \sqrt{3}) - x \sqrt{3} \cdot 5 - x \sqrt{3} (- x \sqrt{3})$

Step 3.1.3

Multiply $5$ by $- 1$ .

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} - x \sqrt{3} (- x \sqrt{3})$

Step 3.1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1.4.1

Move $x$ .

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} - (x \cdot x) \sqrt{3} (- 1 \sqrt{3})$

Step 3.1.4.2

Multiply $x$ by $x$ .

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} - x^{2} \sqrt{3} (- 1 \sqrt{3})$

Step 3.1.5

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

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

Step 3.1.6

Multiply $- x^{2} \sqrt{3} (- \sqrt{3})$ .

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Step 3.1.6.1

Multiply $- 1$ by $- 1$ .

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + 1 x^{2} \sqrt{3} \sqrt{3}$

Step 3.1.6.2

Multiply $x^{2}$ by $1$ .

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} \sqrt{3} \sqrt{3}$

Step 3.1.6.3

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

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} ({\sqrt{3}}^{1} \sqrt{3})$

Step 3.1.6.4

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

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 3.1.6.5

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

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} {\sqrt{3}}^{1 + 1}$

Step 3.1.6.6

Add $1$ and $1$ .

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} {\sqrt{3}}^{2}$

Step 3.1.7

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

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Step 3.1.7.1

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

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} {(3^{\frac{1}{2}})}^{2}$

Step 3.1.7.2

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

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} \cdot 3^{\frac{1}{2} \cdot 2}$

Step 3.1.7.3

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

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} \cdot 3^{\frac{2}{2}}$

Step 3.1.7.4

Cancel the common factor of $2$ .

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Step 3.1.7.4.1

Cancel the common factor.

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} \cdot 3^{\frac{2}{2}}$

Step 3.1.7.4.2

Rewrite the expression.

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} \cdot 3^{1}$

Step 3.1.7.5

Evaluate the exponent.

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + x^{2} \cdot 3$

Step 3.1.8

Move $3$ to the left of $x^{2}$ .

$25 - 5 x \sqrt{3} - 5 x \sqrt{3} + 3 x^{2}$

Step 3.2

Subtract $5 x \sqrt{3}$ from $- 5 x \sqrt{3}$ .

$25 - 10 x \sqrt{3} + 3 x^{2}$