To determine which two expressions are equivalent to \( 2x^2 - 8x - 10 \) when distributed, we can simplify and check each option.
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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: \[ 2x(x - 4x - 5) = 2x(-3x - 5) = -6x^2 - 10x \]
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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 \( 2x^2 - 8x - 10 \).
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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 \( 2x^2 - 8x - 10 \).
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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.
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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.