Algebra Examples

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

Step 1

Expand $(x - 2) (x^{2} + 2 x + 4)$ by multiplying each term in the first expression by each term in the second expression.

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

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 $1$ .

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

Step 2.1.1.1.2

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

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

Step 2.1.1.2

Add $1$ and $2$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

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

Step 2.1.3.2

Multiply $x$ by $x$ .

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

Step 2.1.4

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

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

Step 2.1.5

Multiply $2$ by $- 2$ .

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

Step 2.1.6

Multiply $- 2$ by $4$ .

$x^{3} + 2 x^{2} + 4 x - 2 x^{2} - 4 x - 8$

Step 2.2

Combine the opposite terms in $x^{3} + 2 x^{2} + 4 x - 2 x^{2} - 4 x - 8$ .

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Step 2.2.1

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

$x^{3} + 4 x + 0 - 4 x - 8$

Step 2.2.2

Add $x^{3} + 4 x$ and $0$ .

$x^{3} + 4 x - 4 x - 8$

Step 2.2.3

Subtract $4 x$ from $4 x$ .

$x^{3} + 0 - 8$

Step 2.2.4

Add $x^{3}$ and $0$ .

$x^{3} - 8$