Simplify (3x^4+2x^2-7)-(2x^4-x^3+4x^2)

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

Step 1

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $2$ by $- 1$ .

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

Multiply $- - x^{3}$ .

Multiply $- 1$ by $- 1$ .

$3 x^{4} + 2 x^{2} - 7 - 2 x^{4} + 1 x^{3} - (4 x^{2})$

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

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

Multiply $4$ by $- 1$ .

$3 x^{4} + 2 x^{2} - 7 - 2 x^{4} + x^{3} - 4 x^{2}$

Step 2

Simplify by adding terms.

Subtract $2 x^{4}$ from $3 x^{4}$ .

$x^{4} + 2 x^{2} - 7 + x^{3} - 4 x^{2}$

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

$x^{4} - 2 x^{2} - 7 + x^{3}$

Reorder.

Move $- 7$ .

$x^{4} - 2 x^{2} + x^{3} - 7$

Move $- 2 x^{2}$ .

$x^{4} + x^{3} - 2 x^{2} - 7$