Algebra Examples

$\frac{{(- 2 x)}^{3} {(- x)}^{2}}{{(2 x)}^{2}}$

Step 1

Cancel the common factor of ${(- 2 x)}^{3}$ and ${(2 x)}^{2}$ .

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Step 1.1

Factor $- 1$ out of $- 2 x$ .

$\frac{{(- (2 x))}^{3} {(- x)}^{2}}{{(2 x)}^{2}}$

Step 1.2

Rewrite $- (2 x)$ as $- 1 (2 x)$ .

$\frac{{(- 1 (2 x))}^{3} {(- x)}^{2}}{{(2 x)}^{2}}$

Step 1.3

Apply the product rule to $- 1 (2 x)$ .

$\frac{{(- 1)}^{3} {(2 x)}^{3} {(- x)}^{2}}{{(2 x)}^{2}}$

Step 1.4

Raise $- 1$ to the power of $3$ .

$\frac{- 1 {(2 x)}^{3} {(- x)}^{2}}{{(2 x)}^{2}}$

Step 1.5

Factor ${(2 x)}^{2}$ out of $- 1 {(2 x)}^{3} {(- x)}^{2}$ .

$\frac{{(2 x)}^{2} (- 1 (2 x) {(- x)}^{2})}{{(2 x)}^{2}}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

Multiply by $1$ .

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

Step 1.6.2

Cancel the common factor.

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

Step 1.6.3

Rewrite the expression.

$\frac{- 1 (2 x) {(- x)}^{2}}{1}$

Step 1.6.4

Divide $- 1 (2 x) {(- x)}^{2}$ by $1$ .

$- 1 (2 x) {(- x)}^{2}$

Step 2

Simplify the expression.

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Step 2.1

Multiply $2$ by $- 1$ .

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

Step 2.2

Apply the product rule to $- x$ .

$- 2 x ({(- 1)}^{2} x^{2})$

Step 2.3

Rewrite using the commutative property of multiplication.

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

Step 3

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

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Step 3.1

Move $x^{2}$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $2$ and $1$ .

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

Step 4

Raise $- 1$ to the power of $2$ .

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

Step 5

Multiply $- 2$ by $1$ .

$- 2 x^{3}$