Algebra Examples

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

Step 1

Expand

$(x - 1) (x^{2} + x + 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

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

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Step 2.1.1

Reorder the factors in the terms

$x \cdot 1$ and

$- 1 x$ .

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

Step 2.1.2

Subtract

$1 x$ from

$1 x$ .

$x \cdot x^{2} + x \cdot x - 1 x^{2} + 0 - 1 \cdot 1$

Step 2.1.3

Add

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

$0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply

$x$ by

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

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Step 2.2.1.1

Multiply

$x$ by

$x^{2}$ .

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Step 2.2.1.1.1

Raise

$x$ to the power of

$1$ .

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

Step 2.2.1.1.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2.1.2

Add

$1$ and

$2$ .

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

Step 2.2.2

Multiply

$x$ by

$x$ .

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

Step 2.2.3

Rewrite

$- 1 x^{2}$ as

$- x^{2}$ .

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

Step 2.2.4

Multiply

$- 1$ by

$1$ .

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

Step 2.3

Combine the opposite terms in

$x^{3} + x^{2} - x^{2} - 1$ .

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Step 2.3.1

Subtract

$x^{2}$ from

$x^{2}$ .

$x^{3} + 0 - 1$

Step 2.3.2

Add

$x^{3}$ and

$0$ .

$x^{3} - 1$