Calculate( 5x^3- 2x) ( 3x^2+x-8) .  

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

I guess the two terms have to be multiplied.

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

=> 5x^3*3x^2 + 5x^3*x - 8*5x^3 - 2x*3x^2 - 2x*x + 16x

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

=> 15x^5 + 5x^4 - 46x^3 - 2x^2 + 16x

The product of ( 5x^3- 2x) ( 3x^2+x-8) is 15x^5 + 5x^4 - 46x^3 - 2x^2 + 16x

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll remove the brackets using the distributive property of multiplication 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

We’ve answered 318,912 questions. We can answer yours, too.

Ask a question