Algebra Examples

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

Step 1

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

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $x^{2}$ .

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

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

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

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

Step 2.1.1.3

Add $2$ and $1$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

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

Step 2.1.3.2

Multiply $x$ by $x$ .

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

Step 2.1.4

Multiply $2$ by $- 1$ .

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

Step 2.1.5

Multiply $- 1$ by $2$ .

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

Step 2.1.6

Multiply $- 1$ by $3$ .

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

Step 2.1.7

Multiply $3$ by $- 1$ .

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

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- 2 x^{2}$ and $3 x^{2}$ .

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

Step 2.2.2

Subtract $3 x$ from $- 2 x$ .

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

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