Simplify (5x^3+2xy^2-4y^3)-(10x^3-8xy^2-12y^3)

$(5 x^{3} + 2 x y^{2} - 4 y^{3}) - (10 x^{3} - 8 x y^{2} - 12 y^{3})$

Step 1

Simplify each term.

Apply the distributive property.

$5 x^{3} + 2 x y^{2} - 4 y^{3} - (10 x^{3}) - (- 8 x y^{2}) - (- 12 y^{3})$

Simplify.

Multiply $10$ by $- 1$ .

$5 x^{3} + 2 x y^{2} - 4 y^{3} - 10 x^{3} - (- 8 x y^{2}) - (- 12 y^{3})$

Multiply $- 8$ by $- 1$ .

$5 x^{3} + 2 x y^{2} - 4 y^{3} - 10 x^{3} + 8 (x y^{2}) - (- 12 y^{3})$

Multiply $- 12$ by $- 1$ .

$5 x^{3} + 2 x y^{2} - 4 y^{3} - 10 x^{3} + 8 (x y^{2}) + 12 y^{3}$

$5 x^{3} + 2 x y^{2} - 4 y^{3} - 10 x^{3} + 8 x y^{2} + 12 y^{3}$

Step 2

Simplify by adding terms.

Subtract $10 x^{3}$ from $5 x^{3}$ .

$- 5 x^{3} + 2 x y^{2} - 4 y^{3} + 8 x y^{2} + 12 y^{3}$

Add $2 x y^{2}$ and $8 x y^{2}$ .

$- 5 x^{3} - 4 y^{3} + 10 x y^{2} + 12 y^{3}$

Add $- 4 y^{3}$ and $12 y^{3}$ .

$- 5 x^{3} + 8 y^{3} + 10 x y^{2}$