Pre-Algebra Examples

$- 5 u^{3} + 9 u + (- 5 u^{3} v^{4} - 8 u + 8 u^{2} v^{2}) + (- 8 u^{4} v^{2} + 8 u^{3} v^{4})$

Step 1

Remove parentheses.

$- 5 u^{3} + 9 u - 5 u^{3} v^{4} - 8 u + 8 u^{2} v^{2} - 8 u^{4} v^{2} + 8 u^{3} v^{4}$

Step 2

Subtract $8 u$ from $9 u$ .

$- 5 u^{3} - 5 u^{3} v^{4} + u + 8 u^{2} v^{2} - 8 u^{4} v^{2} + 8 u^{3} v^{4}$

Step 3

Add $- 5 u^{3} v^{4}$ and $8 u^{3} v^{4}$ .

$- 5 u^{3} + 3 u^{3} v^{4} + u + 8 u^{2} v^{2} - 8 u^{4} v^{2}$

Step 4

Factor $u$ out of $- 5 u^{3} + 3 u^{3} v^{4} + u + 8 u^{2} v^{2} - 8 u^{4} v^{2}$ .

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Step 4.1

Factor $u$ out of $- 5 u^{3}$ .

$u (- 5 u^{2}) + 3 u^{3} v^{4} + u + 8 u^{2} v^{2} - 8 u^{4} v^{2}$

Step 4.2

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

$u (- 5 u^{2}) + u (3 u^{2} v^{4}) + u + 8 u^{2} v^{2} - 8 u^{4} v^{2}$

Step 4.3

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

$u (- 5 u^{2}) + u (3 u^{2} v^{4}) + u^{1} + 8 u^{2} v^{2} - 8 u^{4} v^{2}$

Step 4.4

Factor $u$ out of $u^{1}$ .

$u (- 5 u^{2}) + u (3 u^{2} v^{4}) + u \cdot 1 + 8 u^{2} v^{2} - 8 u^{4} v^{2}$

Step 4.5

Factor $u$ out of $8 u^{2} v^{2}$ .

$u (- 5 u^{2}) + u (3 u^{2} v^{4}) + u \cdot 1 + u (8 u v^{2}) - 8 u^{4} v^{2}$

Step 4.6

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

$u (- 5 u^{2}) + u (3 u^{2} v^{4}) + u \cdot 1 + u (8 u v^{2}) + u (- 8 u^{3} v^{2})$

Step 4.7

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

$u (- 5 u^{2} + 3 u^{2} v^{4}) + u \cdot 1 + u (8 u v^{2}) + u (- 8 u^{3} v^{2})$

Step 4.8

Factor $u$ out of $u (- 5 u^{2} + 3 u^{2} v^{4}) + u \cdot 1$ .

$u (- 5 u^{2} + 3 u^{2} v^{4} + 1) + u (8 u v^{2}) + u (- 8 u^{3} v^{2})$

Step 4.9

Factor $u$ out of $u (- 5 u^{2} + 3 u^{2} v^{4} + 1) + u (8 u v^{2})$ .

$u (- 5 u^{2} + 3 u^{2} v^{4} + 1 + 8 u v^{2}) + u (- 8 u^{3} v^{2})$

Step 4.10

Factor $u$ out of $u (- 5 u^{2} + 3 u^{2} v^{4} + 1 + 8 u v^{2}) + u (- 8 u^{3} v^{2})$ .

$u (- 5 u^{2} + 3 u^{2} v^{4} + 1 + 8 u v^{2} - 8 u^{3} v^{2})$