Algebra Examples

$(m n + m^{2} - 2 n^{3}) - (5 m^{2} + 8 m n - 6 n^{3}) + (3 m n - 6 m^{2} + 4 n^{3})$

Step 1

Remove parentheses.

$(m n + m^{2} - 2 n^{3}) - (5 m^{2} + 8 m n - 6 n^{3}) + 3 m n - 6 m^{2} + 4 n^{3}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$m n + m^{2} - 2 n^{3} - (5 m^{2}) - (8 m n) - (- 6 n^{3}) + 3 m n - 6 m^{2} + 4 n^{3}$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Multiply $5$ by $- 1$ .

$m n + m^{2} - 2 n^{3} - 5 m^{2} - (8 m n) - (- 6 n^{3}) + 3 m n - 6 m^{2} + 4 n^{3}$

Step 2.2.2

Multiply $8$ by $- 1$ .

$m n + m^{2} - 2 n^{3} - 5 m^{2} - 8 (m n) - (- 6 n^{3}) + 3 m n - 6 m^{2} + 4 n^{3}$

Step 2.2.3

Multiply $- 6$ by $- 1$ .

$m n + m^{2} - 2 n^{3} - 5 m^{2} - 8 (m n) + 6 n^{3} + 3 m n - 6 m^{2} + 4 n^{3}$

$m n + m^{2} - 2 n^{3} - 5 m^{2} - 8 m n + 6 n^{3} + 3 m n - 6 m^{2} + 4 n^{3}$

Step 3

Simplify by adding terms.

Tap for more steps...

Step 3.1

Subtract $8 m n$ from $m n$ .

$m^{2} - 2 n^{3} - 5 m^{2} - 7 m n + 6 n^{3} + 3 m n - 6 m^{2} + 4 n^{3}$

Step 3.2

Subtract $5 m^{2}$ from $m^{2}$ .

$- 2 n^{3} - 4 m^{2} - 7 m n + 6 n^{3} + 3 m n - 6 m^{2} + 4 n^{3}$

Step 3.3

Add $- 2 n^{3}$ and $6 n^{3}$ .

$4 n^{3} - 4 m^{2} - 7 m n + 3 m n - 6 m^{2} + 4 n^{3}$

Step 3.4

Add $4 n^{3}$ and $4 n^{3}$ .

$8 n^{3} - 4 m^{2} - 7 m n + 3 m n - 6 m^{2}$

Step 3.5

Subtract $6 m^{2}$ from $- 4 m^{2}$ .

$8 n^{3} - 10 m^{2} - 7 m n + 3 m n$

Step 3.6

Add $- 7 m n$ and $3 m n$ .

$8 n^{3} - 10 m^{2} - 4 m n$