Answer:

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

Step-by-step explanation:

The given expression can be factorised as follows:

a² + b² + 2ab + 2bc + 2ac

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

Applying formula,we get  

⇒(a + b)² + 2(bc + ca)  

Looking for common sub-expressions : (a + b)

⇒(a + b)² + 2c(b + a)  

⇒(a + b) (a + b + 2c)  

Can't be factorized any more.

Hence, Final result of a² + b² + 2ab + 2bc + 2ca is (a + b)(a + b + 2c).

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

→The given expression can be factorised as follows:-

→ a²+ b² +2ab+ 2bc + 2ac

→ Using the identify (a+b) 2 = a2 + b2 + 2ab

→ Applying the formula get,

→ (a+b)² +2(bc+ca)

→ looking for common Sub-expressions : (a+b)

→ (a+b)²+ 2c(b+a)

→ (a+b) (a+b+2c)

→ Can't be factorised any more

→ Hence, Final result of a²+ b²+ 2ab+ 2bc+ 2ca is (a+b) (a+b+2c).

hope it's help you