Question

a+b+c whole sqare identity

Answer 1

$\color{pink}\large\underline\mathfrak{Answer:-}$

(a+b+c)² = a²+b²+c²+2ab+2bc+2ca

Or

(a+b+c)² = a²+b²+c²+2(ab+bc+ca)

Answer 2

Taking LHS of the identity:

(a + b +c)2

This can also be written as:

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

Multiply as we do multiplication of trinomials and we get:

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

= a2 + ab + ac + ab + b2 + bc + ac + bc + c2

Rearrange the terms and we get:

= a2 + b2 + c2 + ab + ab + bc + bc + ac + ac

On adding like terms and we get:

= a2 + b2+ c2 + 2ab + 2bc + 2ca

Hence, in this way we obtain the identity i.e. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca