From first to last, order the steps to prove that expression A is equivalent to expression B.

Question

Expression A: (x+4)(x−2)
Expression B: x2+2x−8
Option #1: (x+4)(x−2) (Start)
Option #2: x2−2x+4x−8
Option #3: x2+2x−8
Option #4: x(x)−x(2)+4(x)−4(2)

First: Option # __
Second: Option # __
Third: Option #__
Fourth: Option # __

Answer 1

To prove that expression A, \((x+4)(x−2)\), is equivalent to expression B, \(x^2 + 2x - 8\), we can follow these steps in order:

1. First: Start with the expression A:

   • Option #1: \((x+4)(x−2)\) (Start)

2. Second: Expand the expression using the distributive property:

   • Option #4: \(x(x)−x(2)+4(x)−4(2)\)

3. Third: Combine like terms from the expansion:

   • Option #2: \(x^2−2x+4x−8\) (which simplifies to \(x^2 + 2x - 8\))

4. Fourth: This confirms that the expanded form is equivalent to expression B:

   • Option #3: \(x^2 + 2x - 8\)

So the complete order is:

• First: Option #1
• Second: Option #4
• Third: Option #2
• Fourth: Option #3