Trigonometry Examples

$(x^{2} - 9 x - 3) - (6 x^{2} \cdot (4 x) - 2)$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite using the commutative property of multiplication.

$x^{2} - 9 x - 3 - (6 \cdot 4 x^{2} x - 2)$

Step 1.1.2

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

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Step 1.1.2.1

Move $x$ .

$x^{2} - 9 x - 3 - (6 \cdot 4 (x \cdot x^{2}) - 2)$

Step 1.1.2.2

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

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Step 1.1.2.2.1

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

$x^{2} - 9 x - 3 - (6 \cdot 4 (x^{1} x^{2}) - 2)$

Step 1.1.2.2.2

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

$x^{2} - 9 x - 3 - (6 \cdot 4 x^{1 + 2} - 2)$

Step 1.1.2.3

Add $1$ and $2$ .

$x^{2} - 9 x - 3 - (6 \cdot 4 x^{3} - 2)$

Step 1.1.3

Multiply $6$ by $4$ .

$x^{2} - 9 x - 3 - (24 x^{3} - 2)$

Step 1.2

Apply the distributive property.

$x^{2} - 9 x - 3 - (24 x^{3}) - - 2$

Step 1.3

Multiply $24$ by $- 1$ .

$x^{2} - 9 x - 3 - 24 x^{3} - - 2$

Step 1.4

Multiply $- 1$ by $- 2$ .

$x^{2} - 9 x - 3 - 24 x^{3} + 2$

Step 2

Simplify the expression.

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Step 2.1

Add $- 3$ and $2$ .

$x^{2} - 9 x - 24 x^{3} - 1$

Step 2.2

Move $- 9 x$ .

$x^{2} - 24 x^{3} - 9 x - 1$

Step 2.3

Reorder $x^{2}$ and $- 24 x^{3}$ .

$- 24 x^{3} + x^{2} - 9 x - 1$