Evaluate (x+1/x)^2

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

Rewrite ${(x + \frac{1}{x})}^{2}$ as $(x + \frac{1}{x}) (x + \frac{1}{x})$ .

$(x + \frac{1}{x}) (x + \frac{1}{x})$

Expand $(x + \frac{1}{x}) (x + \frac{1}{x})$ using the FOIL Method.

Apply the distributive property.

$x (x + \frac{1}{x}) + \frac{1}{x} (x + \frac{1}{x})$

Apply the distributive property.

$x \cdot x + x \frac{1}{x} + \frac{1}{x} (x + \frac{1}{x})$

Apply the distributive property.

$x \cdot x + x \frac{1}{x} + \frac{1}{x} x + \frac{1}{x} \cdot \frac{1}{x}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{x} \cdot \frac{1}{x}$ .

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

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

Raise $x$ to the power of $1$ .

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

Raise $x$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Add $1$ and $1$ .

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