Simplify (y^2-3y^3-2+5y)-(7+8y^2-4y+6y^3)

$(y^{2} - 3 y^{3} - 2 + 5 y) - (7 + 8 y^{2} - 4 y + 6 y^{3})$

Step 1

Simplify each term.

Apply the distributive property.

$y^{2} - 3 y^{3} - 2 + 5 y - 1 \cdot 7 - (8 y^{2}) - (- 4 y) - (6 y^{3})$

Simplify.

Multiply $- 1$ by $7$ .

$y^{2} - 3 y^{3} - 2 + 5 y - 7 - (8 y^{2}) - (- 4 y) - (6 y^{3})$

Multiply $8$ by $- 1$ .

$y^{2} - 3 y^{3} - 2 + 5 y - 7 - 8 y^{2} - (- 4 y) - (6 y^{3})$

Multiply $- 4$ by $- 1$ .

$y^{2} - 3 y^{3} - 2 + 5 y - 7 - 8 y^{2} + 4 y - (6 y^{3})$

Multiply $6$ by $- 1$ .

$y^{2} - 3 y^{3} - 2 + 5 y - 7 - 8 y^{2} + 4 y - 6 y^{3}$

Step 2

Simplify by adding terms.

Subtract $8 y^{2}$ from $y^{2}$ .

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

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

$- 7 y^{2} - 9 y^{3} - 2 + 5 y - 7 + 4 y$

Subtract $7$ from $- 2$ .

$- 7 y^{2} - 9 y^{3} + 5 y - 9 + 4 y$

Add $5 y$ and $4 y$ .

$- 7 y^{2} - 9 y^{3} + 9 y - 9$

Reorder $- 7 y^{2}$ and $- 9 y^{3}$ .

$- 9 y^{3} - 7 y^{2} + 9 y - 9$