Pre-Algebra Examples

$2 x^{2} (5 x + 8 x^{3})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$2 x^{2} (5 x) + 2 x^{2} (8 x^{3})$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$2 \cdot 5 x^{2} x + 2 x^{2} (8 x^{3})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$2 \cdot 5 x^{2} x + 2 \cdot 8 x^{2} x^{3}$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

$2 \cdot 5 (x \cdot x^{2}) + 2 \cdot 8 x^{2} x^{3}$

Step 2.1.2

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

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Step 2.1.2.1

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

$2 \cdot 5 (x^{1} x^{2}) + 2 \cdot 8 x^{2} x^{3}$

Step 2.1.2.2

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

$2 \cdot 5 x^{1 + 2} + 2 \cdot 8 x^{2} x^{3}$

Step 2.1.3

Add $1$ and $2$ .

$2 \cdot 5 x^{3} + 2 \cdot 8 x^{2} x^{3}$

Step 2.2

Multiply $2$ by $5$ .

$10 x^{3} + 2 \cdot 8 x^{2} x^{3}$

Step 2.3

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

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Step 2.3.1

Move $x^{3}$ .

$10 x^{3} + 2 \cdot 8 (x^{3} x^{2})$

Step 2.3.2

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

$10 x^{3} + 2 \cdot 8 x^{3 + 2}$

Step 2.3.3

Add $3$ and $2$ .

$10 x^{3} + 2 \cdot 8 x^{5}$

Step 2.4

Multiply $2$ by $8$ .

$10 x^{3} + 16 x^{5}$