Simplify (8x^5+6x^3-2x^2+10x)-(9x^5-x^3-13x^2+4)

$(8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x) - (9 x^{5} - x^{3} - 13 x^{2} + 4)$

Simplify each term.

Apply the distributive property.

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - (9 x^{5}) - - x^{3} - (- 13 x^{2}) - 1 \cdot 4$

Simplify.

Multiply $9$ by $- 1$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} - - x^{3} - (- 13 x^{2}) - 1 \cdot 4$

Multiply $- - x^{3}$ .

Multiply $- 1$ by $- 1$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} + 1 x^{3} - (- 13 x^{2}) - 1 \cdot 4$

Multiply $x^{3}$ by $1$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} + x^{3} - (- 13 x^{2}) - 1 \cdot 4$

Multiply $- 13$ by $- 1$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} + x^{3} + 13 x^{2} - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$8 x^{5} + 6 x^{3} - 2 x^{2} + 10 x - 9 x^{5} + x^{3} + 13 x^{2} - 4$

Simplify by adding terms.

Subtract $9 x^{5}$ from $8 x^{5}$ .

$- x^{5} + 6 x^{3} - 2 x^{2} + 10 x + x^{3} + 13 x^{2} - 4$

Add $6 x^{3}$ and $x^{3}$ .

$- x^{5} + 7 x^{3} - 2 x^{2} + 10 x + 13 x^{2} - 4$

Add $- 2 x^{2}$ and $13 x^{2}$ .

$- x^{5} + 7 x^{3} + 11 x^{2} + 10 x - 4$