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

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

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $3$ by $- 1$ .

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

Multiply $- 2$ by $- 1$ .

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

Multiply $- 4$ by $- 1$ .

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

Multiply $6$ by $- 1$ .

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

Simplify by adding terms.

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

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

$5 x^{4} - 3 x + 0 + 4 x^{3} - 6 x^{4}$

Add $5 x^{4} - 3 x$ and $0$ .

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

Subtract $6 x^{4}$ from $5 x^{4}$ .

$- x^{4} - 3 x + 4 x^{3}$

Move $- 3 x$ .

$- x^{4} + 4 x^{3} - 3 x$