Question

Factorise the following:

8 – 2(x – 1)²

Answer 1

Given: 8 – 2(x – 1)²

Step-wise calculation:

1. Write the expression as:

8 – 2(x – 1)² = 2 × 4 – 2(x – 1)²

8 – 2(x – 1)² = 2[4 – (x – 1)²]

2. Recognize the difference of squares inside the bracket:

4 – (x – 1)² = (2)² – (x – 1)²

4 – (x – 1)² = (2 – (x – 1))(2 + (x – 1))

3. Simplify each factor:

2 – (x – 1) = 2 – x + 1

2 – (x – 1) = 3 – x

2 + (x – 1) = 2 + x – 1

2 + (x – 1) = 1 + x 

4. Substitute back:

2[(3 – x)(1 + x)]

5. Optionally, rewrite as:

2(3 – x)(x + 1)