Simplify (y^3-4y^2-2)-(6y^3+4-6y^2)

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

Step 1

Simplify each term.

Apply the distributive property.

$y^{3} - 4 y^{2} - 2 - (6 y^{3}) - 1 \cdot 4 - (- 6 y^{2})$

Simplify.

Multiply $6$ by $- 1$ .

$y^{3} - 4 y^{2} - 2 - 6 y^{3} - 1 \cdot 4 - (- 6 y^{2})$

Multiply $- 1$ by $4$ .

$y^{3} - 4 y^{2} - 2 - 6 y^{3} - 4 - (- 6 y^{2})$

Multiply $- 6$ by $- 1$ .

$y^{3} - 4 y^{2} - 2 - 6 y^{3} - 4 + 6 y^{2}$

Step 2

Simplify by adding terms.

Subtract $6 y^{3}$ from $y^{3}$ .

$- 5 y^{3} - 4 y^{2} - 2 - 4 + 6 y^{2}$

Add $- 4 y^{2}$ and $6 y^{2}$ .

$- 5 y^{3} + 2 y^{2} - 2 - 4$

Subtract $4$ from $- 2$ .

$- 5 y^{3} + 2 y^{2} - 6$