Question

Factorise the following expression:

− 4a² + 4ab − 4 ca

Answer 1

− 4a² = −1 × 2 × 2 × a × a

4ab = 2 × 2 × a × b

− 4ca = −1 × 2 × 2 × c × a

The common factors are 2, 2, and a.

∴ − 4a² + 4ab − 4ca

= −1 (2 × 2 × a × a) + (2 × 2 × a × b) −1 (2 × 2 × c × a)

= 2 × 2 × a [−1 (a) + b −1 × c]

= 4a (− a + b − c)