Finite Math Examples

$(x^{3} + x^{2} + x + 1) (12 x - 12)$

Step 1

Expand $(x^{3} + x^{2} + x + 1) (12 x - 12)$ by multiplying each term in the first expression by each term in the second expression.

$x^{3} (12 x) + x^{3} \cdot - 12 + x^{2} (12 x) + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$12 x^{3} x + x^{3} \cdot - 12 + x^{2} (12 x) + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$12 (x \cdot x^{3}) + x^{3} \cdot - 12 + x^{2} (12 x) + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.2.2

Multiply $x$ by $x^{3}$ .

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Step 2.1.2.2.1

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

$12 (x^{1} x^{3}) + x^{3} \cdot - 12 + x^{2} (12 x) + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.2.2.2

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

$12 x^{1 + 3} + x^{3} \cdot - 12 + x^{2} (12 x) + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.2.3

Add $1$ and $3$ .

$12 x^{4} + x^{3} \cdot - 12 + x^{2} (12 x) + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.3

Move $- 12$ to the left of $x^{3}$ .

$12 x^{4} - 12 \cdot x^{3} + x^{2} (12 x) + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$12 x^{4} - 12 x^{3} + 12 x^{2} x + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.5

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

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Step 2.1.5.1

Move $x$ .

$12 x^{4} - 12 x^{3} + 12 (x \cdot x^{2}) + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.5.2

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

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Step 2.1.5.2.1

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

$12 x^{4} - 12 x^{3} + 12 (x^{1} x^{2}) + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.5.2.2

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

$12 x^{4} - 12 x^{3} + 12 x^{1 + 2} + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.5.3

Add $1$ and $2$ .

$12 x^{4} - 12 x^{3} + 12 x^{3} + x^{2} \cdot - 12 + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.6

Move $- 12$ to the left of $x^{2}$ .

$12 x^{4} - 12 x^{3} + 12 x^{3} - 12 \cdot x^{2} + x (12 x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$12 x^{4} - 12 x^{3} + 12 x^{3} - 12 x^{2} + 12 x \cdot x + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.8

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

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Step 2.1.8.1

Move $x$ .

$12 x^{4} - 12 x^{3} + 12 x^{3} - 12 x^{2} + 12 (x \cdot x) + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.8.2

Multiply $x$ by $x$ .

$12 x^{4} - 12 x^{3} + 12 x^{3} - 12 x^{2} + 12 x^{2} + x \cdot - 12 + 1 (12 x) + 1 \cdot - 12$

Step 2.1.9

Move $- 12$ to the left of $x$ .

$12 x^{4} - 12 x^{3} + 12 x^{3} - 12 x^{2} + 12 x^{2} - 12 \cdot x + 1 (12 x) + 1 \cdot - 12$

Step 2.1.10

Multiply $12 x$ by $1$ .

$12 x^{4} - 12 x^{3} + 12 x^{3} - 12 x^{2} + 12 x^{2} - 12 x + 12 x + 1 \cdot - 12$

Step 2.1.11

Multiply $- 12$ by $1$ .

$12 x^{4} - 12 x^{3} + 12 x^{3} - 12 x^{2} + 12 x^{2} - 12 x + 12 x - 12$

Step 2.2

Combine the opposite terms in $12 x^{4} - 12 x^{3} + 12 x^{3} - 12 x^{2} + 12 x^{2} - 12 x + 12 x - 12$ .

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Step 2.2.1

Add $- 12 x^{3}$ and $12 x^{3}$ .

$12 x^{4} + 0 - 12 x^{2} + 12 x^{2} - 12 x + 12 x - 12$

Step 2.2.2

Add $12 x^{4}$ and $0$ .

$12 x^{4} - 12 x^{2} + 12 x^{2} - 12 x + 12 x - 12$

Step 2.2.3

Add $- 12 x^{2}$ and $12 x^{2}$ .

$12 x^{4} + 0 - 12 x + 12 x - 12$

Step 2.2.4

Add $12 x^{4}$ and $0$ .

$12 x^{4} - 12 x + 12 x - 12$

Step 2.2.5

Add $- 12 x$ and $12 x$ .

$12 x^{4} + 0 - 12$

Step 2.2.6

Add $12 x^{4}$ and $0$ .

$12 x^{4} - 12$