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

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

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $7$ by $- 1$ .

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

Multiply $4$ by $- 1$ .

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

Multiply $- 5$ by $- 1$ .

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

Multiply $- 1$ by $- 6$ .

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

Simplify by adding terms.

Subtract $7 x^{3}$ from $2 x^{3}$ .

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

Subtract $4 x^{2}$ from $- 7 x^{2}$ .

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

Add $9$ and $6$ .

$4 x^{4} - 5 x^{3} - 11 x^{2} + 5 x + 15$