Pre-Algebra Examples

$3 x (4 x^{2} - 2 x + 5)$

Step 1

Apply the distributive property.

$3 x (4 x^{2}) + 3 x (- 2 x) + 3 x \cdot 5$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 4 x \cdot x^{2} + 3 x (- 2 x) + 3 x \cdot 5$

Step 2.2

Rewrite using the commutative property of multiplication.

$3 \cdot 4 x \cdot x^{2} + 3 \cdot - 2 x \cdot x + 3 x \cdot 5$

Step 2.3

Multiply $5$ by $3$ .

$3 \cdot 4 x \cdot x^{2} + 3 \cdot - 2 x \cdot x + 15 x$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x^{2}$ .

$3 \cdot 4 (x^{2} x) + 3 \cdot - 2 x \cdot x + 15 x$

Step 3.1.2

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

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Step 3.1.2.1

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

$3 \cdot 4 (x^{2} x^{1}) + 3 \cdot - 2 x \cdot x + 15 x$

Step 3.1.2.2

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

$3 \cdot 4 x^{2 + 1} + 3 \cdot - 2 x \cdot x + 15 x$

Step 3.1.3

Add $2$ and $1$ .

$3 \cdot 4 x^{3} + 3 \cdot - 2 x \cdot x + 15 x$

Step 3.2

Multiply $3$ by $4$ .

$12 x^{3} + 3 \cdot - 2 x \cdot x + 15 x$

Step 3.3

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

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Step 3.3.1

Move $x$ .

$12 x^{3} + 3 \cdot - 2 (x \cdot x) + 15 x$

Step 3.3.2

Multiply $x$ by $x$ .

$12 x^{3} + 3 \cdot - 2 x^{2} + 15 x$

Step 3.4

Multiply $3$ by $- 2$ .

$12 x^{3} - 6 x^{2} + 15 x$