find factorisation of b^2+c^2+2(ab+bc+ca)

 find factorisation of b^2+c^2+2(ab+bc+ca) 

Factorise: a² + b² + c² + 2(ab + bc + ca)

Step 1: Open the bracket

a² + b² + c² + 2ab + 2bc + 2ca

Step 2: Recall the identity

(x + y + z)²

= x² + y² + z² + 2xy + 2yz + 2zx

Step 3: Compare with the given expression

a² + b² + c² + 2ab + 2bc + 2ca

Here,

x = a, y = b, z = c

Therefore,

a² + b² + c² + 2ab + 2bc + 2ca

= (a + b + c)²

Final Answer:

(a + b + c)²