Simplify (5x^6-2x^4+9x^3+2x-4)-(7x^5-8x^4+2x-11)

$(5 x^{6} - 2 x^{4} + 9 x^{3} + 2 x - 4) - (7 x^{5} - 8 x^{4} + 2 x - 11)$

Simplify each term.

Apply the distributive property.

$5 x^{6} - 2 x^{4} + 9 x^{3} + 2 x - 4 - (7 x^{5}) - (- 8 x^{4}) - (2 x) - - 11$

Simplify.

Multiply $7$ by $- 1$ .

$5 x^{6} - 2 x^{4} + 9 x^{3} + 2 x - 4 - 7 x^{5} - (- 8 x^{4}) - (2 x) - - 11$

Multiply $- 8$ by $- 1$ .

$5 x^{6} - 2 x^{4} + 9 x^{3} + 2 x - 4 - 7 x^{5} + 8 x^{4} - (2 x) - - 11$

Multiply $2$ by $- 1$ .

$5 x^{6} - 2 x^{4} + 9 x^{3} + 2 x - 4 - 7 x^{5} + 8 x^{4} - 2 x - - 11$

Multiply $- 1$ by $- 11$ .

$5 x^{6} - 2 x^{4} + 9 x^{3} + 2 x - 4 - 7 x^{5} + 8 x^{4} - 2 x + 11$

Simplify by adding terms.

Combine the opposite terms in $5 x^{6} - 2 x^{4} + 9 x^{3} + 2 x - 4 - 7 x^{5} + 8 x^{4} - 2 x + 11$ .

Subtract $2 x$ from $2 x$ .

$5 x^{6} - 2 x^{4} + 9 x^{3} - 4 - 7 x^{5} + 8 x^{4} + 0 + 11$

Add $5 x^{6} - 2 x^{4} + 9 x^{3} - 4 - 7 x^{5} + 8 x^{4}$ and $0$ .

$5 x^{6} - 2 x^{4} + 9 x^{3} - 4 - 7 x^{5} + 8 x^{4} + 11$

Add $- 2 x^{4}$ and $8 x^{4}$ .

$5 x^{6} + 6 x^{4} + 9 x^{3} - 4 - 7 x^{5} + 11$

Simplify the expression.

Add $- 4$ and $11$ .

$5 x^{6} + 6 x^{4} + 9 x^{3} - 7 x^{5} + 7$

Move $9 x^{3}$ .

$5 x^{6} + 6 x^{4} - 7 x^{5} + 9 x^{3} + 7$

Move $6 x^{4}$ .

$5 x^{6} - 7 x^{5} + 6 x^{4} + 9 x^{3} + 7$