Pre-Algebra Examples

$\frac{14 u^{6} - 10 u^{5} + 6 u^{4}}{2 u^{2}}$

Step 1

Factor $2 u^{4}$ out of $14 u^{6} - 10 u^{5} + 6 u^{4}$ .

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Step 1.1

Factor $2 u^{4}$ out of $14 u^{6}$ .

$\frac{2 u^{4} (7 u^{2}) - 10 u^{5} + 6 u^{4}}{2 u^{2}}$

Step 1.2

Factor $2 u^{4}$ out of $- 10 u^{5}$ .

$\frac{2 u^{4} (7 u^{2}) + 2 u^{4} (- 5 u) + 6 u^{4}}{2 u^{2}}$

Step 1.3

Factor $2 u^{4}$ out of $6 u^{4}$ .

$\frac{2 u^{4} (7 u^{2}) + 2 u^{4} (- 5 u) + 2 u^{4} (3)}{2 u^{2}}$

Step 1.4

Factor $2 u^{4}$ out of $2 u^{4} (7 u^{2}) + 2 u^{4} (- 5 u)$ .

$\frac{2 u^{4} (7 u^{2} - 5 u) + 2 u^{4} (3)}{2 u^{2}}$

Step 1.5

Factor $2 u^{4}$ out of $2 u^{4} (7 u^{2} - 5 u) + 2 u^{4} (3)$ .

$\frac{2 u^{4} (7 u^{2} - 5 u + 3)}{2 u^{2}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\frac{2 u^{4} (7 u^{2} - 5 u + 3)}{2 u^{2}}$

Step 2.2

Rewrite the expression.

$\frac{u^{4} (7 u^{2} - 5 u + 3)}{u^{2}}$

Step 3

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

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Step 3.1

Factor $u^{2}$ out of $u^{4} (7 u^{2} - 5 u + 3)$ .

$\frac{u^{2} (u^{2} (7 u^{2} - 5 u + 3))}{u^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{u^{2} (u^{2} (7 u^{2} - 5 u + 3))}{u^{2} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{u^{2} (u^{2} (7 u^{2} - 5 u + 3))}{u^{2} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{u^{2} (7 u^{2} - 5 u + 3)}{1}$

Step 3.2.4

Divide $u^{2} (7 u^{2} - 5 u + 3)$ by $1$ .

$u^{2} (7 u^{2} - 5 u + 3)$

Step 4

Apply the distributive property.

$u^{2} (7 u^{2}) + u^{2} (- 5 u) + u^{2} \cdot 3$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$7 u^{2} u^{2} + u^{2} (- 5 u) + u^{2} \cdot 3$

Step 5.2

Rewrite using the commutative property of multiplication.

$7 u^{2} u^{2} - 5 u^{2} u + u^{2} \cdot 3$

Step 5.3

Move $3$ to the left of $u^{2}$ .

$7 u^{2} u^{2} - 5 u^{2} u + 3 \cdot u^{2}$

Step 6

Simplify each term.

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Step 6.1

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

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Step 6.1.1

Move $u^{2}$ .

$7 (u^{2} u^{2}) - 5 u^{2} u + 3 \cdot u^{2}$

Step 6.1.2

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

$7 u^{2 + 2} - 5 u^{2} u + 3 \cdot u^{2}$

Step 6.1.3

Add $2$ and $2$ .

$7 u^{4} - 5 u^{2} u + 3 \cdot u^{2}$

Step 6.2

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

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Step 6.2.1

Move $u$ .

$7 u^{4} - 5 (u \cdot u^{2}) + 3 \cdot u^{2}$

Step 6.2.2

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

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Step 6.2.2.1

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

$7 u^{4} - 5 (u^{1} u^{2}) + 3 \cdot u^{2}$

Step 6.2.2.2

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

$7 u^{4} - 5 u^{1 + 2} + 3 \cdot u^{2}$

Step 6.2.3

Add $1$ and $2$ .

$7 u^{4} - 5 u^{3} + 3 \cdot u^{2}$

$7 u^{4} - 5 u^{3} + 3 u^{2}$