Pre-Algebra Examples

$- x (2 x^{2} - 4 x) - 6 x^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- x (2 x^{2}) - x (- 4 x) - 6 x^{2}$

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $x^{2}$ .

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

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

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

Step 1.4.1.2.2

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

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

Step 1.4.1.3

Add $2$ and $1$ .

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

Step 1.4.2

Multiply $- 1$ by $2$ .

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

Step 1.4.3

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

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Step 1.4.3.1

Move $x$ .

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

Step 1.4.3.2

Multiply $x$ by $x$ .

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

Step 1.4.4

Multiply $- 1$ by $- 4$ .

$- 2 x^{3} + 4 x^{2} - 6 x^{2}$

Step 2

Subtract $6 x^{2}$ from $4 x^{2}$ .

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