Simplify (x^2-1/x)(x^3+2x)

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

Step 1

Expand $(x^{2} - \frac{1}{x}) (x^{3} + 2 x)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify each term.

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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

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

Add $2$ and $3$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{1}{x}$ into the numerator.

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

Factor $x$ out of $x^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{1}{x}$ into the numerator.

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

Factor $x$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $2$ .

$x^{5} + 2 x^{3} - x^{2} - 2$

Simplify (x^2-1/x)(x^3+2x)

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