What is ( 5x^3- 2x) ( 3x^2+x-8) ?

The given expression is a product of the factors that are
2 pairs of brackets.

We'll remove the brackets knowing the
fact that multiplication of numbers is distributive over addition of
numbers.

( 5x^3- 2x) ( 3x^2+x-8) = 5x^3( 3x^2+x-8) - 2x(
3x^2+x-8)

We'll remove the brackets from the 1st resulted
terms:

5x^3( 3x^2+x-8) = 5x^3*3x^2 + 5x^3*x -
5x^3*8

5x^3( 3x^2+x-8) = 15*x^(3+2) + 5*x^(3+1) -
40x^3

5x^3( 3x^2+x-8) = 15*x^5 + 5*x^4 - 40x^3
(1)

We'll remove the brackets from the 2nd resulted
terms:

- 2x( 3x^2+x-8) = -2x*3x^2 - 2x*x +
16x

- 2x( 3x^2+x-8) = -6x^3 - 2x^2 + 16x
(2)

We'll add (1) +
(2):

15*x^5 + 5*x^4 - 40x^3 - 6x^3 - 2x^2 +
16x

We'll combine like
terms:

(5x^3- 2x) (3x^2+x-8) = 15x^5 + 5x^4 -
46x^3 - 2x^2 + 16x