Algebra Examples

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

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

Expand $(x - 1) (x + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $x \cdot x + x \cdot 1 - 1 x - 1 \cdot 1$ .

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Step 3.1.1

Reorder the factors in the terms $x \cdot 1$ and $- 1 x$ .

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

Step 3.1.2

Subtract $1 x$ from $1 x$ .

$(x \cdot x + 0 - 1 \cdot 1) (x - 3)$

Step 3.1.3

Add $x \cdot x$ and $0$ .

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

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x$ by $x$ .

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

Step 3.2.2

Multiply $- 1$ by $1$ .

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

Step 4

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

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Step 4.1

Apply the distributive property.

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

Step 4.2

Apply the distributive property.

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

Step 4.3

Apply the distributive property.

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

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

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

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Step 5.1.1.1

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

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

Step 5.1.1.2

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

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

Step 5.1.2

Add $2$ and $1$ .

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

Step 5.2

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

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

Step 5.3

Rewrite $- 1 x$ as $- x$ .

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

Step 5.4

Multiply $- 1$ by $- 3$ .

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