Identify two expressions will be equivalent to 2x to the power of 2 - 8x - 10 when distributed. Enter the option with 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 answer

To determine which of the provided options are equivalent to the expression \( 2x^2 - 8x - 10 \), we can simplify or distribute each option:

Option 1: \( 2x (x - 4x - 5) = 2x(-3x - 5) = -6x^2 - 10x \) (Not equivalent)
Option 2: \( (2x + 2)(x - 5) = 2x(x - 5) + 2(x - 5) = 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \) (Equivalent)
Option 3: \( 2x(x - 5) + 2(x - 5) = 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \) (Equivalent)
Option 4: \( (x - 5)(x - 3) = x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \) (Not equivalent)
Option 5: \(-6x - 10\) (Not equivalent)

The two equivalent expressions to \( 2x^2 - 8x - 10 \) are Option 2 and Option 3.

Therefore, the two expressions, entered with the lesser number first, are: