Identify two expressions that will be equivalent to 2x2−8x−10 when distributed. Enter the option with the lesser number first.

Question

Option #1: 2x(x−4x−5)

Option #2: (2x+2)(x−5)

Option #3: 2x(x−5)+2(x−5)

Option #4: (x−5)(x−3)

Option #5: −6x−10

Answer 1

To find the expressions that are equivalent to \( 2x^2 - 8x - 10 \) when distributed, we need to evaluate each option after distributing (if applicable).

1. Option #1: \( 2x(x - 4x - 5) \)
   This expression seems to have a typographical error. Assuming it meant \( 2x(x - 4)(x - 5) \), we will leave it as is for now.

2. Option #2: \( (2x + 2)(x - 5) \)
   Distributing:
   \[ (2x + 2)(x - 5) = 2x(x) + 2(x) - 2x(5) - 2(5) = 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \]
   This option is equivalent to \( 2x^2 - 8x - 10 \).

3. Option #3: \( 2x(x - 5) + 2(x - 5) \)
   Distributing:
   \[ 2x(x - 5) + 2(x - 5) = 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \]
   This option is also equivalent to \( 2x^2 - 8x - 10 \).

4. Option #4: \( (x - 5)(x - 3) \)
   Distributing:
   \[ (x - 5)(x - 3) = x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \]
   This option is not equivalent to \( 2x^2 - 8x - 10 \).

5. Option #5: \( -6x - 10 \)
   This is a linear expression and not equivalent at all to the quadratic expression given.

Considering the evaluated options, the two expressions that are equivalent to \( 2x^2 - 8x - 10 \) are Option #2 and Option #3.

Now, putting the option with the lesser number first:

Answer: Option #2 and Option #3.