Precalculus Examples

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

Step 1

Expand $(2 x^{2} - x - 3) (x + 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $x$ .

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

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

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

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

Step 2.1.1.3

Add $1$ and $2$ .

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

Step 2.1.2

Multiply $2$ by $1$ .

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

Step 2.1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.3.1

Move $x$ .

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

Step 2.1.3.2

Multiply $x$ by $x$ .

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

Step 2.1.4

Multiply $- 1$ by $1$ .

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

Step 2.1.5

Multiply $- 3$ by $1$ .

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

Step 2.2

Simplify by adding terms.

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Step 2.2.1

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

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

Step 2.2.2

Subtract $3 x$ from $- x$ .

$2 x^{3} + x^{2} - 4 x - 3$