Question

Factorize: a²  + b²  + 2 (ab + bc + ca)

Answer 1

= a² + b² + 2ab + 2bc + 2ca

Using identity a2 + b2 + 2ab = (a + b)²

We get,

= (a + b)² + 2bc + 2ca

= (a + b)² + 2c (b + a)

or (a + b)² + 2c (a + b)

Taking (a + b) common

= (a + b)(a + b + 2c )

∴ a² + b² + 2 (ab + bc + ca) = (a + b)(a + b + 2c)