Algebra Examples

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

Step 1

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

$(\sqrt{x} - 1) (\sqrt{x} - 1)$

Step 2

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

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Step 2.1

Apply the distributive property.

$\sqrt{x} (\sqrt{x} - 1) - 1 (\sqrt{x} - 1)$

Step 2.2

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} \cdot - 1 - 1 (\sqrt{x} - 1)$

Step 2.3

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} \cdot - 1 - 1 \sqrt{x} - 1 \cdot - 1$

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 $\sqrt{x} \sqrt{x}$ .

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Step 3.1.1.1

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

${\sqrt{x}}^{1} \sqrt{x} + \sqrt{x} \cdot - 1 - 1 \sqrt{x} - 1 \cdot - 1$

Step 3.1.1.2

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

${\sqrt{x}}^{1} {\sqrt{x}}^{1} + \sqrt{x} \cdot - 1 - 1 \sqrt{x} - 1 \cdot - 1$

Step 3.1.1.3

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

${\sqrt{x}}^{1 + 1} + \sqrt{x} \cdot - 1 - 1 \sqrt{x} - 1 \cdot - 1$

Step 3.1.1.4

Add $1$ and $1$ .

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

Step 3.1.2

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

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Step 3.1.2.1

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

${(x^{\frac{1}{2}})}^{2} + \sqrt{x} \cdot - 1 - 1 \sqrt{x} - 1 \cdot - 1$

Step 3.1.2.2

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

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

Step 3.1.2.3

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

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

Step 3.1.2.4

Cancel the common factor of $2$ .

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Step 3.1.2.4.1

Cancel the common factor.

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

Step 3.1.2.4.2

Rewrite the expression.

$x^{1} + \sqrt{x} \cdot - 1 - 1 \sqrt{x} - 1 \cdot - 1$

Step 3.1.2.5

Simplify.

$x + \sqrt{x} \cdot - 1 - 1 \sqrt{x} - 1 \cdot - 1$

Step 3.1.3

Move $- 1$ to the left of $\sqrt{x}$ .

$x - 1 \cdot \sqrt{x} - 1 \sqrt{x} - 1 \cdot - 1$

Step 3.1.4

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

$x - \sqrt{x} - 1 \sqrt{x} - 1 \cdot - 1$

Step 3.1.5

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

$x - \sqrt{x} - \sqrt{x} - 1 \cdot - 1$

Step 3.1.6

Multiply $- 1$ by $- 1$ .

$x - \sqrt{x} - \sqrt{x} + 1$

Step 3.2

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

$x - 2 \sqrt{x} + 1$