Finite Math Examples

$(2 a^{3} + 3 b^{3}) - (3 a^{2} b - 5 a b^{2} + 3 b^{3} + 2 a^{3})$

Step 1

Apply the distributive property.

$2 a^{3} + 3 b^{3} - (3 a^{2} b) - (- 5 a b^{2}) - (3 b^{3}) - (2 a^{3})$

Step 2

Simplify.

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Step 2.1

Multiply $3$ by $- 1$ .

$2 a^{3} + 3 b^{3} - 3 (a^{2} b) - (- 5 a b^{2}) - (3 b^{3}) - (2 a^{3})$

Step 2.2

Multiply $- 5$ by $- 1$ .

$2 a^{3} + 3 b^{3} - 3 (a^{2} b) + 5 (a b^{2}) - (3 b^{3}) - (2 a^{3})$

Step 2.3

Multiply $3$ by $- 1$ .

$2 a^{3} + 3 b^{3} - 3 (a^{2} b) + 5 (a b^{2}) - 3 b^{3} - (2 a^{3})$

Step 2.4

Multiply $2$ by $- 1$ .

$2 a^{3} + 3 b^{3} - 3 (a^{2} b) + 5 (a b^{2}) - 3 b^{3} - 2 a^{3}$

Step 3

Simplify each term.

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Step 3.1

Remove parentheses.

$2 a^{3} + 3 b^{3} - 3 a^{2} b + 5 (a b^{2}) - 3 b^{3} - 2 a^{3}$

Step 3.2

Remove parentheses.

$2 a^{3} + 3 b^{3} - 3 a^{2} b + 5 a b^{2} - 3 b^{3} - 2 a^{3}$

Step 4

Subtract $2 a^{3}$ from $2 a^{3}$ .

$3 b^{3} - 3 a^{2} b + 5 a b^{2} - 3 b^{3} + 0$

Step 5

Add $3 b^{3} - 3 a^{2} b + 5 a b^{2} - 3 b^{3}$ and $0$ .

$3 b^{3} - 3 a^{2} b + 5 a b^{2} - 3 b^{3}$

Step 6

Subtract $3 b^{3}$ from $3 b^{3}$ .

$- 3 a^{2} b + 5 a b^{2} + 0$

Step 7

Add $- 3 a^{2} b + 5 a b^{2}$ and $0$ .

$- 3 a^{2} b + 5 a b^{2}$

Step 8

Factor $- a b$ out of $- 3 a^{2} b + 5 a b^{2}$ .

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Step 8.1

Factor $- a b$ out of $- 3 a^{2} b$ .

$- a b (3 a) + 5 a b^{2}$

Step 8.2

Factor $- a b$ out of $5 a b^{2}$ .

$- a b (3 a) - a b (- 5 b)$

Step 8.3

Factor $- a b$ out of $- a b (3 a) - a b (- 5 b)$ .

$- a b (3 a - 5 b)$