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

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

Step 1

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $2$ by $- 1$ .

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

Multiply $- 4$ by $- 1$ .

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

Multiply $- 1$ by $- 3$ .

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

Step 2

Simplify by adding terms.

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

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

Simplify the expression.

Add $- 7$ and $3$ .

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

Move $2 x^{2}$ .

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

Move $- 5 x^{3}$ .

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