What is the euivalent expression for (x – 1)(x + 1)-(x + 2)(x – 2)?

Question

A teacher is following the student work shown below. The student was attempting to find an equivalent expression for (x – 1)(x + 1)-(x + 2)(x – 2).

Step 1: (x – 1)(x + 1) – (x – 2)(x + 2) = ( x2 – 1) – (x2 – 4)

 

Step 2: (x2 – 1) – (x2 – 4) = x2 – 1 – x2 – 4

 

Step 3: x2 – 1 – x2 – 4 = x2 – x2 – 1 – 4

 

Step 4: x2 – x2 – 1 – 4 = - 5

Answer 1

Step 2: Negative is not correctly distributed.

 

(x - 1)(x + 1) - (x + 2)(x - 2)

x² - 1 - (x² - 4)

x² - 1 - x² + 4

3