Trigonometry Examples

$- 3 x (4 x^{2} - 6 x + 12)$

Step 1

Apply the distributive property.

$- 3 x (4 x^{2}) - 3 x (- 6 x) - 3 x \cdot 12$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- 3 \cdot 4 x \cdot x^{2} - 3 x (- 6 x) - 3 x \cdot 12$

Step 2.2

Rewrite using the commutative property of multiplication.

$- 3 \cdot 4 x \cdot x^{2} - 3 \cdot - 6 x \cdot x - 3 x \cdot 12$

Step 2.3

Multiply $12$ by $- 3$ .

$- 3 \cdot 4 x \cdot x^{2} - 3 \cdot - 6 x \cdot x - 36 x$

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 $x^{2}$ .

$- 3 \cdot 4 (x^{2} x) - 3 \cdot - 6 x \cdot x - 36 x$

Step 3.1.2

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

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Step 3.1.2.1

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

$- 3 \cdot 4 (x^{2} x^{1}) - 3 \cdot - 6 x \cdot x - 36 x$

Step 3.1.2.2

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

$- 3 \cdot 4 x^{2 + 1} - 3 \cdot - 6 x \cdot x - 36 x$

Step 3.1.3

Add $2$ and $1$ .

$- 3 \cdot 4 x^{3} - 3 \cdot - 6 x \cdot x - 36 x$

Step 3.2

Multiply $- 3$ by $4$ .

$- 12 x^{3} - 3 \cdot - 6 x \cdot x - 36 x$

Step 3.3

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

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Step 3.3.1

Move $x$ .

$- 12 x^{3} - 3 \cdot - 6 (x \cdot x) - 36 x$

Step 3.3.2

Multiply $x$ by $x$ .

$- 12 x^{3} - 3 \cdot - 6 x^{2} - 36 x$

Step 3.4

Multiply $- 3$ by $- 6$ .

$- 12 x^{3} + 18 x^{2} - 36 x$