Calculus Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

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

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Step 2.1.1.1

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

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

Step 2.1.1.2

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

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

Step 2.1.2

Add $2$ and $1$ .

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

Step 2.2

Move $- 1$ to the left of $x^{2}$ .

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

Step 2.3

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

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

Step 2.4

Multiply $x$ by $1$ .

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

Step 2.5

Multiply $- 1$ by $1$ .

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