Question

Choose the correct simplification of the expression (3x − 6)(2x2 − 4x − 5).

6x3 − 24x2 + 9x − 30
6x3 + 9x + 30
6x3 − 24x2 + 9x + 30
6x3 − 24x2 + 39x + 30

Answer 1

(3x×2x^2)+(3x×-4x)+(3x×-5)+(-6×2x^2)+(-6×-4x)+(-6×-5)
so, (6x^3)+(-12x^2)+(-15x)+(-12x^2)+(24x)+(30)

-12x^2can be added to the other -12x^2, which is =-24x^2
same thing with -15x and 24x that =9x

final answer
6x^3-24x^2+9x+30

Answer 2

The correct option is C. 6x³ - 24x² + 9x + 30

Explanation:

The equation which is to be simplified :

(3x − 6)(2x² − 4x − 5)

Now, to simplify using the distributive law of multiplication over addition

⇒ 3x(2x² − 4x − 5) - 6(2x² − 4x − 5)

Again, By distributive law, we have :

⇒ 6x³ - 12x² - 15x - 12x² + 24x + 30

⇒ 6x³ - 12x² - 12x² - 15x + 24x + 30

⇒ 6x³ - 24x² + 9x + 30

Hence, The correct option is C. 6x³ - 24x² + 9x + 30