Basic Math Examples

$2 r^{3} - 3 r + (2 r + 7 r^{4}) - (8 r - 5 r^{4})$

Step 1

Remove parentheses.

$2 r^{3} - 3 r + 2 r + 7 r^{4} - (8 r - 5 r^{4})$

Step 2

Factor $r$ out of $2 r^{3} - 3 r$ .

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Step 2.1

Factor $r$ out of $2 r^{3}$ .

$r (2 r^{2}) - 3 r + 2 r + 7 r^{4} - (8 r - 5 r^{4})$

Step 2.2

Factor $r$ out of $- 3 r$ .

$r (2 r^{2}) + r \cdot - 3 + 2 r + 7 r^{4} - (8 r - 5 r^{4})$

Step 2.3

Factor $r$ out of $r (2 r^{2}) + r \cdot - 3$ .

$r (2 r^{2} - 3) + 2 r + 7 r^{4} - (8 r - 5 r^{4})$

Step 3

Apply the distributive property.

$r (2 r^{2} - 3) + 2 r + 7 r^{4} - (8 r) - (- 5 r^{4})$

Step 4

Multiply $8$ by $- 1$ .

$r (2 r^{2} - 3) + 2 r + 7 r^{4} - 8 r - (- 5 r^{4})$

Step 5

Multiply $- 5$ by $- 1$ .

$r (2 r^{2} - 3) + 2 r + 7 r^{4} - 8 r + 5 r^{4}$

Step 6

Subtract $8 r$ from $2 r$ .

$r (2 r^{2} - 3) + 7 r^{4} - 6 r + 5 r^{4}$

Step 7

Add $7 r^{4}$ and $5 r^{4}$ .

$r (2 r^{2} - 3) + 12 r^{4} - 6 r$

Step 8

Factor $6 r$ out of $12 r^{4} - 6 r$ .

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Step 8.1

Factor $6 r$ out of $12 r^{4}$ .

$r (2 r^{2} - 3) + 6 r (2 r^{3}) - 6 r$

Step 8.2

Factor $6 r$ out of $- 6 r$ .

$r (2 r^{2} - 3) + 6 r (2 r^{3}) + 6 r (- 1)$

Step 8.3

Factor $6 r$ out of $6 r (2 r^{3}) + 6 r (- 1)$ .

$r (2 r^{2} - 3) + 6 r (2 r^{3} - 1)$

Step 9

Factor $r$ out of $r (2 r^{2} - 3) + 6 r (2 r^{3} - 1)$ .

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Step 9.1

Factor $r$ out of $6 r (2 r^{3} - 1)$ .

$r (2 r^{2} - 3) + r (6 (2 r^{3} - 1))$

Step 9.2

Factor $r$ out of $r (2 r^{2} - 3) + r (6 (2 r^{3} - 1))$ .

$r (2 r^{2} - 3 + 6 (2 r^{3} - 1))$

Step 10

Apply the distributive property.

$r (2 r^{2} - 3 + 6 (2 r^{3}) + 6 \cdot - 1)$

Step 11

Multiply $2$ by $6$ .

$r (2 r^{2} - 3 + 12 r^{3} + 6 \cdot - 1)$

Step 12

Multiply $6$ by $- 1$ .

$r (2 r^{2} - 3 + 12 r^{3} - 6)$

Step 13

Subtract $6$ from $- 3$ .

$r (2 r^{2} + 12 r^{3} - 9)$

Step 14

Reorder terms.

$r (12 r^{3} + 2 r^{2} - 9)$