Use the Distributive Property to find which expression is equivalent to x2−2x−8

Question

(x+2)(x−4)
left parenthesis x plus 2 right parenthesis left parenthesis x minus 4 right parenthesis

(x+2)(x+4)
left parenthesis x plus 2 right parenthesis left parenthesis x plus 4 right parenthesis

(x+4)(x−2)
left parenthesis x plus 4 right parenthesis left parenthesis x minus 2 right parenthesis

(x+4)(x−4)

Answer 1

To find which expression is equivalent to \( x^2 - 2x - 8 \) using the Distributive Property, we can expand each option provided.

1. Option: \((x + 2)(x - 4)\) \[ (x + 2)(x - 4) = x^2 - 4x + 2x - 8 = x^2 - 2x - 8 \] This matches \( x^2 - 2x - 8 \).

2. Option: \((x + 2)(x + 4)\) \[ (x + 2)(x + 4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8 \] This does not match.

3. Option: \((x + 4)(x - 2)\) \[ (x + 4)(x - 2) = x^2 - 2x + 4x - 8 = x^2 + 2x - 8 \] This does not match.

4. Option: \((x + 4)(x - 4)\) \[ (x + 4)(x - 4) = x^2 - 16 \] This does not match.

The only expression that is equivalent to \( x^2 - 2x - 8 \) is:

\[ \boxed{(x + 2)(x - 4)} \]