Simplify (6a^5+a^2-5b^3)-(3a^3+6a^2-2b^3)

$(6 a^{5} + a^{2} - 5 b^{3}) - (3 a^{3} + 6 a^{2} - 2 b^{3})$

Step 1

Simplify each term.

Apply the distributive property.

$6 a^{5} + a^{2} - 5 b^{3} - (3 a^{3}) - (6 a^{2}) - (- 2 b^{3})$

Simplify.

Multiply $3$ by $- 1$ .

$6 a^{5} + a^{2} - 5 b^{3} - 3 a^{3} - (6 a^{2}) - (- 2 b^{3})$

Multiply $6$ by $- 1$ .

$6 a^{5} + a^{2} - 5 b^{3} - 3 a^{3} - 6 a^{2} - (- 2 b^{3})$

Multiply $- 2$ by $- 1$ .

$6 a^{5} + a^{2} - 5 b^{3} - 3 a^{3} - 6 a^{2} + 2 b^{3}$

Step 2

Simplify by adding terms.

Subtract $6 a^{2}$ from $a^{2}$ .

$6 a^{5} - 5 b^{3} - 3 a^{3} - 5 a^{2} + 2 b^{3}$

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

$6 a^{5} - 3 b^{3} - 3 a^{3} - 5 a^{2}$