Question

Factorize: a² + b² + 2(ab + bc + ca).

Answer 1

a² + b² + 2ab + 2bc + 2ca 

As we know, p² + q² + 2pq = (p + q)² 

We get,

= (a+b)² + 2bc + 2ca 

= (a+b)² + 2c( b + a ) 

Or (a+b)² + 2c( a + b ) 

Take (a + b) as common factor; 

= (a + b)(a + b + 2c) 

Therefore, a² + b² + 2ab + 2bc + 2ca 

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