Simplify (6x+3x^3-5)-(5x^3+2x^2-3x-8)

$(6 x + 3 x^{3} - 5) - (5 x^{3} + 2 x^{2} - 3 x - 8)$

Step 1

Simplify each term.

Apply the distributive property.

$6 x + 3 x^{3} - 5 - (5 x^{3}) - (2 x^{2}) - (- 3 x) - - 8$

Simplify.

Multiply $5$ by $- 1$ .

$6 x + 3 x^{3} - 5 - 5 x^{3} - (2 x^{2}) - (- 3 x) - - 8$

Multiply $2$ by $- 1$ .

$6 x + 3 x^{3} - 5 - 5 x^{3} - 2 x^{2} - (- 3 x) - - 8$

Multiply $- 3$ by $- 1$ .

$6 x + 3 x^{3} - 5 - 5 x^{3} - 2 x^{2} + 3 x - - 8$

Multiply $- 1$ by $- 8$ .

$6 x + 3 x^{3} - 5 - 5 x^{3} - 2 x^{2} + 3 x + 8$

Step 2

Simplify by adding terms.

Add $6 x$ and $3 x$ .

$3 x^{3} - 5 - 5 x^{3} - 2 x^{2} + 9 x + 8$

Subtract $5 x^{3}$ from $3 x^{3}$ .

$- 2 x^{3} - 5 - 2 x^{2} + 9 x + 8$

Add $- 5$ and $8$ .

$- 2 x^{3} - 2 x^{2} + 9 x + 3$