Question

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

6x3 − 24x2 + 6x + 36
6x3 − 24x2 + 6x − 36
6x3 + 24x2 − 6x + 36
6x3 − 24x2 + 6x + 12

Answer 1

Option A is correct.

Correct simplification of the given expression =
`6x^3-24x^2+6x+36`

Explanation:

Given the expression:
`(2x-6)(3x^2-3x-6)`

The following steps required for the multiplication of polynomials are:

• Distribute each terms of the first polynomial to every term of the second polynomial.

• Combine like terms

Apply these steps to the given expressions;

`2x(3x^2-3x-6) -6(3x^2-3x-6)`

when you multiply two terms together you must multiply the coefficient (numbers) and add the exponent.

⇒
`6x^3-6x^2-12x -18x^2 +18x +36`

Combine like terms;

`6x^3-24x^2+6x+36`

Therefore, the correct simplification of the given expression is,
`6x^3-24x^2+6x+36`

Answer 2

If you would like to solve (2x - 6) * (3x^2 - 3x - 6), you can do this using the following steps:

(2x - 6) * (3x^2 - 3x - 6) = 2x * 3x^2 - 2x * 3x - 2x * 6 - 6 * 3x^2 + 6 * 3x + 6 * 6 = 6x^3 - 6x^2 - 12x - 18x^2 + 18x + 36 = 6x^3 - 24x^2 + 6x + 36

The correct result would be 6x^3 - 24x^2 + 6x + 36.