Pre-Algebra Examples

$\frac{10 u^{4} + 4 u^{3}}{- u^{2}}$

Step 1

Factor $2 u^{3}$ out of $10 u^{4} + 4 u^{3}$ .

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Step 1.1

Factor $2 u^{3}$ out of $10 u^{4}$ .

$\frac{2 u^{3} (5 u) + 4 u^{3}}{- u^{2}}$

Step 1.2

Factor $2 u^{3}$ out of $4 u^{3}$ .

$\frac{2 u^{3} (5 u) + 2 u^{3} (2)}{- u^{2}}$

Step 1.3

Factor $2 u^{3}$ out of $2 u^{3} (5 u) + 2 u^{3} (2)$ .

$\frac{2 u^{3} (5 u + 2)}{- u^{2}}$

Step 2

Cancel the common factor of $u^{3}$ and $u^{2}$ .

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Step 2.1

Factor $u^{2}$ out of $2 u^{3} (5 u + 2)$ .

$\frac{u^{2} (2 u (5 u + 2))}{- u^{2}}$

Step 2.2

Move the negative one from the denominator of $\frac{2 u (5 u + 2)}{- 1}$ .

$- 1 \cdot (2 u (5 u + 2))$

Step 3

Rewrite $- 1 \cdot (2 u (5 u + 2))$ as $- (2 u (5 u + 2))$ .

$- (2 u (5 u + 2))$

Step 4

Apply the distributive property.

$- (2 u (5 u) + 2 u \cdot 2)$

Step 5

Rewrite using the commutative property of multiplication.

$- (2 \cdot 5 u \cdot u + 2 u \cdot 2)$

Step 6

Multiply $2$ by $2$ .

$- (2 \cdot 5 u \cdot u + 4 u)$

Step 7

Simplify each term.

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Step 7.1

Multiply $u$ by $u$ by adding the exponents.

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Step 7.1.1

Move $u$ .

$- (2 \cdot 5 (u \cdot u) + 4 u)$

Step 7.1.2

Multiply $u$ by $u$ .

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

Step 7.2

Multiply $2$ by $5$ .

$- (10 u^{2} + 4 u)$

Step 8

Apply the distributive property.

$- (10 u^{2}) - (4 u)$

Step 9

Multiply $10$ by $- 1$ .

$- 10 u^{2} - (4 u)$

Step 10

Multiply $4$ by $- 1$ .

$- 10 u^{2} - 4 u$