Algebra Examples

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

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

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Simplify the expression.

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Step 2.2.1

Multiply $x$ by $x$ .

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

Step 2.2.2

Move $4$ to the left of $x$ .

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

Step 3

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

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Step 3.1

Apply the distributive property.

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

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

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Step 4.1.1.1.1

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

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

Step 4.1.1.1.2

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

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

Step 4.1.1.2

Add $2$ and $1$ .

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

Step 4.1.2

Move $- 3$ to the left of $x^{2}$ .

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

Step 4.1.3

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

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Step 4.1.3.1

Move $x$ .

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

Step 4.1.3.2

Multiply $x$ by $x$ .

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

Step 4.1.4

Multiply $- 3$ by $4$ .

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

Step 4.2

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

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