Algebra Examples

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

Step 1

Multiply the expressions.

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

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

Step 3.1.2

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

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Step 3.1.2.1

Move $x^{3}$ .

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

Step 3.1.2.2

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

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

Step 3.1.2.3

Add $3$ and $3$ .

$- x^{6} + x^{3} \cdot - 3 + 3 x (- x^{3}) + 3 x \cdot - 3 + 3 (- x^{3}) + 3 \cdot - 3$

Step 3.1.3

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

$- x^{6} - 3 \cdot x^{3} + 3 x (- x^{3}) + 3 x \cdot - 3 + 3 (- x^{3}) + 3 \cdot - 3$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$- x^{6} - 3 x^{3} + 3 \cdot - 1 x \cdot x^{3} + 3 x \cdot - 3 + 3 (- x^{3}) + 3 \cdot - 3$

Step 3.1.5

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

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Step 3.1.5.1

Move $x^{3}$ .

$- x^{6} - 3 x^{3} + 3 \cdot - 1 (x^{3} x) + 3 x \cdot - 3 + 3 (- x^{3}) + 3 \cdot - 3$

Step 3.1.5.2

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

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Step 3.1.5.2.1

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

$- x^{6} - 3 x^{3} + 3 \cdot - 1 (x^{3} x^{1}) + 3 x \cdot - 3 + 3 (- x^{3}) + 3 \cdot - 3$

Step 3.1.5.2.2

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

$- x^{6} - 3 x^{3} + 3 \cdot - 1 x^{3 + 1} + 3 x \cdot - 3 + 3 (- x^{3}) + 3 \cdot - 3$

Step 3.1.5.3

Add $3$ and $1$ .

$- x^{6} - 3 x^{3} + 3 \cdot - 1 x^{4} + 3 x \cdot - 3 + 3 (- x^{3}) + 3 \cdot - 3$

Step 3.1.6

Multiply $3$ by $- 1$ .

$- x^{6} - 3 x^{3} - 3 x^{4} + 3 x \cdot - 3 + 3 (- x^{3}) + 3 \cdot - 3$

Step 3.1.7

Multiply $- 3$ by $3$ .

$- x^{6} - 3 x^{3} - 3 x^{4} - 9 x + 3 (- x^{3}) + 3 \cdot - 3$

Step 3.1.8

Multiply $- 1$ by $3$ .

$- x^{6} - 3 x^{3} - 3 x^{4} - 9 x - 3 x^{3} + 3 \cdot - 3$

Step 3.1.9

Multiply $3$ by $- 3$ .

$- x^{6} - 3 x^{3} - 3 x^{4} - 9 x - 3 x^{3} - 9$

Step 3.2

Simplify by adding terms.

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Step 3.2.1

Subtract $3 x^{3}$ from $- 3 x^{3}$ .

$- x^{6} - 6 x^{3} - 3 x^{4} - 9 x - 9$

Step 3.2.2

Move $- 6 x^{3}$ .

$- x^{6} - 3 x^{4} - 6 x^{3} - 9 x - 9$

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