Simplify (2x^3+3x^2-x-5)-(x^3-2x^2+5x-1)

$(2 x^{3} + 3 x^{2} - x - 5) - (x^{3} - 2 x^{2} + 5 x - 1)$

Step 1

Simplify each term.

Apply the distributive property.

$2 x^{3} + 3 x^{2} - x - 5 - x^{3} - (- 2 x^{2}) - (5 x) - - 1$

Simplify.

Multiply $- 2$ by $- 1$ .

$2 x^{3} + 3 x^{2} - x - 5 - x^{3} + 2 x^{2} - (5 x) - - 1$

Multiply $5$ by $- 1$ .

$2 x^{3} + 3 x^{2} - x - 5 - x^{3} + 2 x^{2} - 5 x - - 1$

Multiply $- 1$ by $- 1$ .

$2 x^{3} + 3 x^{2} - x - 5 - x^{3} + 2 x^{2} - 5 x + 1$

Step 2

Simplify by adding terms.

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

$x^{3} + 3 x^{2} - x - 5 + 2 x^{2} - 5 x + 1$

Add $3 x^{2}$ and $2 x^{2}$ .

$x^{3} + 5 x^{2} - x - 5 - 5 x + 1$

Subtract $5 x$ from $- x$ .

$x^{3} + 5 x^{2} - 6 x - 5 + 1$

Add $- 5$ and $1$ .

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