Question

Simplify the expression 2(x + 7)(x2 − 3x − 6). 2x3 − 28x2 − 18x − 84 2x3 − 18x2 − 28x − 84 2x3 + 8x2 − 54x − 84 2x3 + 4x2 − 27x − 42

Answer 1

The answer is C, 2x^3 + 8x^2 - 54x - 84. (I took a test and got this correct)

Explanation:

Distribute the 2 to the numbers in parenthesis.

The equation should now look like this.

(2x + 14)(x^2 - 3x - 6)

Multiply the right side by the left side, here are the results I got.

2x * x^2 = 2x^3

2x * -3x = -6x^2

2x * -6 = -12x

14 * x^2 = 14x^2

14 * -3x = -42x

14 * -6 = -84.

Now assemble the new equation.

2x^3 - 6x^2 + 14x^2 - 42x - 12x - 84

Now combine like terms.

2x^3 - 8x^2 - 54x - 84

Hope this helps you!

Answer 2

The correct option is C)
`2x^3+8x^2-54x-84`.

Explanation:

Consider the provided expression.

`2(x + 7)(x^2-3x-6)`

Use the distributive property:

`a(b+c)=ab+ac`

By using the above property we can simplify it as shown:

`(2x + 14)(x^2-3x-6)`

Use the distributive property.

`2x^3-6x^2-12x+14x^2-42x-84`

Add and subtract the like terms.

`2x^3+8x^2-54x-84`

Thus, the simplified form of the provided expression is
`2x^3+8x^2-54x-84`.

Hence, the correct option is C)
`2x^3+8x^2-54x-84`.