Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $1$ by $1$ .

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

Step 3.1.2

Multiply $- \sqrt{x}$ by $1$ .

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

Step 3.1.3

Multiply $- 1$ by $1$ .

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

Step 3.1.4

Multiply $- \sqrt{x} (- \sqrt{x})$ .

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.4.2

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

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

Step 3.1.4.3

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

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

Step 3.1.4.4

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

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

Step 3.1.4.5

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

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

Step 3.1.4.6

Add $1$ and $1$ .

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

Step 3.1.5

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

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Step 3.1.5.1

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

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

Step 3.1.5.2

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

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

Step 3.1.5.3

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

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

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.

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

Step 3.1.5.4.2

Rewrite the expression.

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

Step 3.1.5.5

Simplify.

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

Step 3.2

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

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