Question

Factorise the following:

75a²b² – 108c²

Answer 1

The given expression is,

75a²b² – 108c²

= 3(25a²b² – 36c²)

Here we use the identity,

x² – y² = (x + y)(x – y)

Taking x = 5ab and y = 6c, we get

∴ 75a²b² – 36c²

= 3((5ab)² – (6c)²)

= 3(5ab – 6c)(5ab + 6c)

Therefore, the factors of the given expression are 3(5ab – 6c)(5ab + 6c)