Question

Factorise : (a² − b²) c + (b² − c²)a 

Answer 1

(a² − b²) c + (b² − c²)a

Use the difference of squares formula: 

x² − y² = (x − y)(x + y)

Apply this to both a² − b² and b²−c².

1. a² − b² = (a − b)(a + b)
2. b² − c² = (b − c)(b + c)

Substitute these into the expression:

(a² − b²) c + (b² − c²) a = (a − b) (a + b) c + (b − c) (b + c) a

Group the expression by factoring out common terms later:

(a − b) c (a+b) + (b − c) a (b + c)

(a² − b²) c + (b² − c²) a