Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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

Step 2.1.1.2

Add $2$ and $3$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

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

Step 2.1.3.2

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

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Step 2.1.3.2.1

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

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

Step 2.1.3.2.2

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

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

Step 2.1.3.3

Add $1$ and $2$ .

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

Step 2.1.4

Rewrite $- 1 x^{3}$ as $- x^{3}$ .

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

Step 2.1.5

Multiply $2$ by $- 1$ .

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

Step 2.2

Subtract $x^{3}$ from $2 x^{3}$ .

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