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


(1 point)

Answer 1

number 1 is not correct

Answer 2

To find expressions equivalent to \( 2x^2 - 8x - 10 \) when distributed, we need to rewrite or simplify the given options and see which ones match the original expression. Let’s distribute each option to compare their forms:

1. **Option #1:** \( 2x(x - 4x - 5) \)
- This seems to be written incorrectly. If we assume it means \( 2x(x - 4) - 5 \):
- Distributing:
\[
2x(x - 4) - 10 = 2x^2 - 8x - 10
\]
- So this is equivalent.

2. **Option #2:** \( (2x + 2)(x - 5) \)
- Distributing:
\[
2x(x) + 2(-5) + 2x(-5) = 2x^2 - 10 + 2x(-5) = 2x^2 - 10 + 10x
\]
Simplifying:
\[
2x^2 - 8x - 10 \text{ (not equivalent)}
\]

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

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

5. **Option #5:** \( -6x - 10 \)
- This doesn’t contain an \( x^2 \) term and cannot be equivalent.

Considering these calculations, the expressions that are equivalent to \( 2x^2 - 8x - 10 \) are:

- Option #1: \( 2x(x - 4) - 10 \)
- Option #3: \( 2x(x - 5) + 2(x - 5) \)

Thus, the two expressions are **Option #1** and **Option #3**. Since we need to enter them in order with the lesser number first, we will write:

**Option #1: 2x(x - 4) - 10; Option #3: 2x(x - 5) + 2(x - 5)**

Make sure to check the actual content of Option #1 as the way it was written did not seem complete.

Answer 3

Let's carefully revisit the evaluation of the options against the expression \( 2x^2 - 8x - 10 \). We'll go through each option step-by-step to find which ones are equivalent to \( 2x^2 - 8x - 10 \):

### Given Expression:
\[
2x^2 - 8x - 10
\]

### Evaluating Each Option:

1. **Option #1:** \( 2x(x - 4x - 5) \)
- This expression seems incorrectly formed due to extra terms in the parentheses. If we treat it as \( 2x(x - 4 - 5) \):
- Note: Rewriting it correctly gives us \( 2x(x - 4 - 5) = 2x(x - 9) \), which simplifies to:
\[
2x^2 - 18x \quad (\text{not equivalent})
\]

2. **Option #2:** \( (2x + 2)(x - 5) \)
- Distributing:
\[
= 2x \cdot x + 2 \cdot x - 2x \cdot 5 - 2 \cdot 5
\]
Simplifying:
\[
= 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \quad (\text{equivalent})
\]

3. **Option #3:** \( 2x(x - 5) + 2(x - 5) \)
- Distributing:
\[
2x(x - 5) + 2(x - 5) = 2x^2 - 10x + 2x - 10
\]
Simplifying:
\[
= 2x^2 - 8x - 10 \quad (\text{equivalent})
\]

4. **Option #4:** \( (x - 5)(x - 3) \)
- Distributing:
\[
= x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \quad (\text{not equivalent})
\]

5. **Option #5:** \( -6x - 10 \)
- This expression doesn’t have the \( x^2 \) term, so it cannot be equivalent.

### Conclusion:
The two options that are equivalent to \( 2x^2 - 8x - 10 \) are:

- **Option #2:** \( (2x + 2)(x - 5) \)
- **Option #3:** \( 2x(x - 5) + 2(x - 5) \)

### Final Answer:
The correct pairs (with the lesser number first) are:

- **Option #2:** (2x + 2)(x - 5)
- **Option #3:** 2x(x - 5) + 2(x - 5)

Thank you for your patience, and I hope this clears up any confusion!