Algebra Examples

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

Step 1

Expand $(3 - x) (3 x^{2} + x - 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $3$ by $3$ .

$9 x^{2} + 3 x + 3 \cdot - 4 - x (3 x^{2}) - x \cdot x - x \cdot - 4$

Step 2.1.2

Multiply $3$ by $- 4$ .

$9 x^{2} + 3 x - 12 - x (3 x^{2}) - x \cdot x - x \cdot - 4$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$9 x^{2} + 3 x - 12 - 1 \cdot 3 x \cdot x^{2} - x \cdot x - x \cdot - 4$

Step 2.1.4

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

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Step 2.1.4.1

Move $x^{2}$ .

$9 x^{2} + 3 x - 12 - 1 \cdot 3 (x^{2} x) - x \cdot x - x \cdot - 4$

Step 2.1.4.2

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

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Step 2.1.4.2.1

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

$9 x^{2} + 3 x - 12 - 1 \cdot 3 (x^{2} x^{1}) - x \cdot x - x \cdot - 4$

Step 2.1.4.2.2

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

$9 x^{2} + 3 x - 12 - 1 \cdot 3 x^{2 + 1} - x \cdot x - x \cdot - 4$

Step 2.1.4.3

Add $2$ and $1$ .

$9 x^{2} + 3 x - 12 - 1 \cdot 3 x^{3} - x \cdot x - x \cdot - 4$

Step 2.1.5

Multiply $- 1$ by $3$ .

$9 x^{2} + 3 x - 12 - 3 x^{3} - x \cdot x - x \cdot - 4$

Step 2.1.6

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

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Step 2.1.6.1

Move $x$ .

$9 x^{2} + 3 x - 12 - 3 x^{3} - (x \cdot x) - x \cdot - 4$

Step 2.1.6.2

Multiply $x$ by $x$ .

$9 x^{2} + 3 x - 12 - 3 x^{3} - x^{2} - x \cdot - 4$

Step 2.1.7

Multiply $- 4$ by $- 1$ .

$9 x^{2} + 3 x - 12 - 3 x^{3} - x^{2} + 4 x$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $x^{2}$ from $9 x^{2}$ .

$8 x^{2} + 3 x - 12 - 3 x^{3} + 4 x$

Step 2.2.2

Add $3 x$ and $4 x$ .

$8 x^{2} + 7 x - 12 - 3 x^{3}$

Step 2.2.3

Simplify the expression.

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Step 2.2.3.1

Move $- 12$ .

$8 x^{2} + 7 x - 3 x^{3} - 12$

Step 2.2.3.2

Move $7 x$ .

$8 x^{2} - 3 x^{3} + 7 x - 12$

Step 2.2.3.3

Reorder $8 x^{2}$ and $- 3 x^{3}$ .

$- 3 x^{3} + 8 x^{2} + 7 x - 12$