Pre-Algebra Examples

$\frac{25 u^{5} - 8 u^{4}}{4 u^{2}}$

Step 1

Factor $u^{4}$ out of $25 u^{5} - 8 u^{4}$ .

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Step 1.1

Factor $u^{4}$ out of $25 u^{5}$ .

$\frac{u^{4} (25 u) - 8 u^{4}}{4 u^{2}}$

Step 1.2

Factor $u^{4}$ out of $- 8 u^{4}$ .

$\frac{u^{4} (25 u) + u^{4} \cdot - 8}{4 u^{2}}$

Step 1.3

Factor $u^{4}$ out of $u^{4} (25 u) + u^{4} \cdot - 8$ .

$\frac{u^{4} (25 u - 8)}{4 u^{2}}$

Step 2

Cancel the common factor of $u^{4}$ and $u^{2}$ .

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Step 2.1

Factor $u^{2}$ out of $u^{4} (25 u - 8)$ .

$\frac{u^{2} (u^{2} (25 u - 8))}{4 u^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{u^{2} (u^{2} (25 u - 8))}{u^{2} \cdot 4}$

Step 2.2.2

Cancel the common factor.

$\frac{u^{2} (u^{2} (25 u - 8))}{u^{2} \cdot 4}$

Step 2.2.3

Rewrite the expression.

$\frac{u^{2} (25 u - 8)}{4}$

Step 3

Apply the distributive property.

$\frac{u^{2} (25 u) + u^{2} \cdot - 8}{4}$

Step 4

Rewrite using the commutative property of multiplication.

$\frac{25 u^{2} u + u^{2} \cdot - 8}{4}$

Step 5

Move $- 8$ to the left of $u^{2}$ .

$\frac{25 u^{2} u - 8 \cdot u^{2}}{4}$

Step 6

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

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Step 6.1

Move $u$ .

$\frac{25 (u \cdot u^{2}) - 8 \cdot u^{2}}{4}$

Step 6.2

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

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Step 6.2.1

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

$\frac{25 (u^{1} u^{2}) - 8 \cdot u^{2}}{4}$

Step 6.2.2

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

$\frac{25 u^{1 + 2} - 8 \cdot u^{2}}{4}$

Step 6.3

Add $1$ and $2$ .

$\frac{25 u^{3} - 8 \cdot u^{2}}{4}$

$\frac{25 u^{3} - 8 u^{2}}{4}$

Step 7

Split the fraction $\frac{25 u^{3} - 8 u^{2}}{4}$ into two fractions.

$\frac{25 u^{3}}{4} + \frac{- 8 u^{2}}{4}$

Step 8

Cancel the common factor of $- 8$ and $4$ .

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Step 8.1

Factor $4$ out of $- 8 u^{2}$ .

$\frac{25 u^{3}}{4} + \frac{4 (- 2 u^{2})}{4}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $4$ out of $4$ .

$\frac{25 u^{3}}{4} + \frac{4 (- 2 u^{2})}{4 (1)}$

Step 8.2.2

Cancel the common factor.

$\frac{25 u^{3}}{4} + \frac{4 (- 2 u^{2})}{4 \cdot 1}$

Step 8.2.3

Rewrite the expression.

$\frac{25 u^{3}}{4} + \frac{- 2 u^{2}}{1}$

Step 8.2.4

Divide $- 2 u^{2}$ by $1$ .

$\frac{25 u^{3}}{4} - 2 u^{2}$