Algebra Examples

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

Step 1

Expand $(4 - x) (x^{2} - 3 x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 3$ by $4$ .

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x^{2}$ .

$4 x^{2} - 12 x - (x^{2} x) - x (- 3 x)$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

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

Step 2.1.2.2.2

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

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

Step 2.1.2.3

Add $2$ and $1$ .

$4 x^{2} - 12 x - x^{3} - x (- 3 x)$

Step 2.1.3

Rewrite using the commutative property of multiplication.

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

Step 2.1.4

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

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Step 2.1.4.1

Move $x$ .

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

Step 2.1.4.2

Multiply $x$ by $x$ .

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

Step 2.1.5

Multiply $- 1$ by $- 3$ .

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

Step 2.2

Add $4 x^{2}$ and $3 x^{2}$ .

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

Step 3

Move $- 12 x$ .

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

Step 4

Reorder $7 x^{2}$ and $- x^{3}$ .

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