Algebra Examples

$2 x (3 - x + 5 x^{2})$

Step 1

Apply the distributive property.

$2 x \cdot 3 + 2 x (- x) + 2 x (5 x^{2})$

Step 2

Simplify.

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Step 2.1

Multiply $3$ by $2$ .

$6 x + 2 x (- x) + 2 x (5 x^{2})$

Step 2.2

Rewrite using the commutative property of multiplication.

$6 x + 2 \cdot - 1 x \cdot x + 2 x (5 x^{2})$

Step 2.3

Rewrite using the commutative property of multiplication.

$6 x + 2 \cdot - 1 x \cdot x + 2 \cdot 5 x \cdot x^{2}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x$ .

$6 x + 2 \cdot - 1 (x \cdot x) + 2 \cdot 5 x \cdot x^{2}$

Step 3.1.2

Multiply $x$ by $x$ .

$6 x + 2 \cdot - 1 x^{2} + 2 \cdot 5 x \cdot x^{2}$

Step 3.2

Multiply $2$ by $- 1$ .

$6 x - 2 x^{2} + 2 \cdot 5 x \cdot x^{2}$

Step 3.3

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

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Step 3.3.1

Move $x^{2}$ .

$6 x - 2 x^{2} + 2 \cdot 5 (x^{2} x)$

Step 3.3.2

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

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Step 3.3.2.1

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

$6 x - 2 x^{2} + 2 \cdot 5 (x^{2} x^{1})$

Step 3.3.2.2

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

$6 x - 2 x^{2} + 2 \cdot 5 x^{2 + 1}$

Step 3.3.3

Add $2$ and $1$ .

$6 x - 2 x^{2} + 2 \cdot 5 x^{3}$

Step 3.4

Multiply $2$ by $5$ .

$6 x - 2 x^{2} + 10 x^{3}$