Algebra Examples

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

Step 1

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

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

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

Step 2.1.1.1.2

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

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

Step 2.1.1.2

Add $1$ and $2$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

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

Step 2.1.3.2

Multiply $x$ by $x$ .

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

Step 2.1.4

Move $2$ to the left of $x$ .

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

Step 2.1.5

Multiply $- 1$ by $- 2$ .

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

Step 2.1.6

Multiply $- 2$ by $2$ .

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

Step 2.2

Simplify terms.

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Step 2.2.1

Subtract $2 x^{2}$ from $- x^{2}$ .

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

Step 2.2.2

Add $2 x$ and $2 x$ .

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

Step 2.2.3

Apply the distributive property.

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

Step 3

Simplify.

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Step 3.1

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

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Step 3.1.1

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

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

Step 3.1.2

Add $3$ and $3$ .

$x^{6} - 3 x^{2} x^{3} + 4 x \cdot x^{3} - 4 x^{3}$

Step 3.2

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 3.2.1

Move $x^{3}$ .

$x^{6} - 3 (x^{3} x^{2}) + 4 x \cdot x^{3} - 4 x^{3}$

Step 3.2.2

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

$x^{6} - 3 x^{3 + 2} + 4 x \cdot x^{3} - 4 x^{3}$

Step 3.2.3

Add $3$ and $2$ .

$x^{6} - 3 x^{5} + 4 x \cdot x^{3} - 4 x^{3}$

Step 3.3

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 3.3.1

Move $x^{3}$ .

$x^{6} - 3 x^{5} + 4 (x^{3} x) - 4 x^{3}$

Step 3.3.2

Multiply $x^{3}$ by $x$ .

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Step 3.3.2.1

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

$x^{6} - 3 x^{5} + 4 (x^{3} x^{1}) - 4 x^{3}$

Step 3.3.2.2

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

$x^{6} - 3 x^{5} + 4 x^{3 + 1} - 4 x^{3}$

Step 3.3.3

Add $3$ and $1$ .

$x^{6} - 3 x^{5} + 4 x^{4} - 4 x^{3}$