Algebra Examples

$3 x (x + 4) (x - 1)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Apply the distributive property.

$(3 x \cdot x + 3 x \cdot 4) (x - 1)$

Step 3

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

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Step 3.1

Move $x$ .

$(3 (x \cdot x) + 3 x \cdot 4) (x - 1)$

Step 3.2

Multiply $x$ by $x$ .

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

Step 4

Multiply $4$ by $3$ .

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

Step 5

Expand $(3 x^{2} + 12 x) (x - 1)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Apply the distributive property.

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

Step 5.3

Apply the distributive property.

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

Step 6

Simplify and combine like terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

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

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Step 6.1.1.1

Move $x$ .

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

Step 6.1.1.2

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

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Step 6.1.1.2.1

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

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

Step 6.1.1.2.2

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

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

Step 6.1.1.3

Add $1$ and $2$ .

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

Step 6.1.2

Multiply $- 1$ by $3$ .

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

Step 6.1.3

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

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Step 6.1.3.1

Move $x$ .

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

Step 6.1.3.2

Multiply $x$ by $x$ .

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

Step 6.1.4

Multiply $- 1$ by $12$ .

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

Step 6.2

Add $- 3 x^{2}$ and $12 x^{2}$ .

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