Question

Factorise a^2+b^2+2ab+2bc+2ca

Answer 1

a² + b² + 2ab + 2bc + 2ac

We know, x² + y² + 2xy = (x + y)

Applying formula,we get

(a + b)² + 2(bc + ca)

(a + b)² + 2c(b + a)

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

Can't be factorized any more.

Answer 2

a^2 + b^2 + 2ab + 2bc + 2ca

= [ a^2 + b^2 + 2(a)(b)] + 2c( a + b)

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

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