Simplify (2x^3-x+5)-(6x^3+x^2-x+1)

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

Step 1

Simplify each term.

Apply the distributive property.

$2 x^{3} - x + 5 - (6 x^{3}) - x^{2} - - x - 1 \cdot 1$

Simplify.

Multiply $6$ by $- 1$ .

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

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 1$ by $1$ .

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

Step 2

Simplify by adding terms.

Combine the opposite terms in $2 x^{3} - x + 5 - 6 x^{3} - x^{2} + x - 1$ .

Add $- x$ and $x$ .

$2 x^{3} + 5 - 6 x^{3} - x^{2} + 0 - 1$

Add $2 x^{3} + 5 - 6 x^{3} - x^{2}$ and $0$ .

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

Subtract $6 x^{3}$ from $2 x^{3}$ .

$- 4 x^{3} + 5 - x^{2} - 1$

Subtract $1$ from $5$ .

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