Question

Factorise the following:

4x² – a² + 2a – 1

Answer 1

Given expression: 4x² – a² + 2a – 1

Step-wise calculation:

1. Rearrange and group the terms:

4x² – (a² – 2a + 1)

2. Recognize the terms inside the parentheses as a perfect square:

a² – 2a + 1 = (a – 1)²

3. Substitute to get a difference of squares:

4x² – (a – 1)²

4. Use the identity A² – B² = (A – B)(A + B), where A = 2x, B = (a – 1)

5. So: 4x² – (a – 1)² = (2x – (a – 1))(2x + (a – 1))

6. Simplify the factors: (2x – a + 1)(2x + a – 1)