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 (1 point) Option # and Option #. What’s the answer

Answer 1

To determine which options might be equivalent or provide a related answer, we can simplify each of the given options.

**Option #1: \( 2x(x - 4x - 5) \)**
1. Simplify inside the parentheses:
\[ x - 4x - 5 = -3x - 5 \]
2. Expanding:
\[ 2x(-3x - 5) = -6x^2 - 10x \]

**Option #2: \( (2x + 2)(x - 5) \)**
1. Expand:
\[ 2x \cdot x - 5(2x) + 2 \cdot x - 5 \cdot 2 = 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \]

**Option #3: \( 2x(x - 5) + 2(x - 5) \)**
1. Factor out \( (x - 5) \):
\[ (2x + 2)(x - 5) \]
2. Expanding (which is the same as Option #2):
\[ 2x^2 - 8x - 10 \]

**Option #4: \( (x - 5)(x - 3) \)**
1. Expand:
\[ x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \]

**Option #5: \( -6x - 10 \)**
This is already simplified.

Now we can summarize the simplified results:
- Option #1: \( -6x^2 - 10x \)
- Option #2: \( 2x^2 - 8x - 10 \)
- Option #3: \( 2x^2 - 8x - 10 \)
- Option #4: \( x^2 - 8x + 15 \)
- Option #5: \( -6x - 10 \)

From the above simplifications, we see that:
- Option #2 and Option #3 are equal.

So the answer is:
**Option #2 and Option #3.**