Finite Math Examples

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

Step 1

Expand $(3 x - 1) (x^{2} - 5 x - 2)$ by multiplying each term in the first expression by each term in the second expression.

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

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 $x^{2}$ .

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

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 $1$ .

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

Step 2.1.1.2.2

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

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

Step 2.1.1.3

Add $2$ and $1$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

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

Step 2.1.3.2

Multiply $x$ by $x$ .

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

Step 2.1.4

Multiply $3$ by $- 5$ .

$3 x^{3} - 15 x^{2} + 3 x \cdot - 2 - 1 x^{2} - 1 (- 5 x) - 1 \cdot - 2$

Step 2.1.5

Multiply $- 2$ by $3$ .

$3 x^{3} - 15 x^{2} - 6 x - 1 x^{2} - 1 (- 5 x) - 1 \cdot - 2$

Step 2.1.6

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

$3 x^{3} - 15 x^{2} - 6 x - x^{2} - 1 (- 5 x) - 1 \cdot - 2$

Step 2.1.7

Multiply $- 5$ by $- 1$ .

$3 x^{3} - 15 x^{2} - 6 x - x^{2} + 5 x - 1 \cdot - 2$

Step 2.1.8

Multiply $- 1$ by $- 2$ .

$3 x^{3} - 15 x^{2} - 6 x - x^{2} + 5 x + 2$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $x^{2}$ from $- 15 x^{2}$ .

$3 x^{3} - 16 x^{2} - 6 x + 5 x + 2$

Step 2.2.2

Add $- 6 x$ and $5 x$ .

$3 x^{3} - 16 x^{2} - x + 2$