Question

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

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 determine which two expressions are equivalent to \( 2x^2 - 8x - 10 \) when distributed, we can simplify and check each option.

1. **Option #1: \( 2x(x - 4x - 5) \)**
- This expression has a misplacement of parentheses. It should read \( 2x(x - 4) - 10 \) or something similar. Let's calculate:
\[
2x(x - 4x - 5) = 2x(-3x - 5) = -6x^2 - 10x
\]

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

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

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

5. **Option #5: \( -6x - 10 \)**
- This is just a linear expression and not quadratic; thus, it does not match.

The two equivalent expressions are **Option #2: \( (2x + 2)(x - 5) \)** and **Option #3: \( 2x(x - 5) + 2(x - 5) \)**.

Thus, the option with the lesser number first is:

**Option #2**, **Option #3**.