Question

verify the algebric identity

(a+b)2=a2+b2+c2+2ab+2bc+2ca

Answer 1

this formula is not correct
(a+b)^2 = a^2 +b^2+ 2ab & 
(a +b+ c)^2 =a^2 + b^2 + c^2 +2(ab+bc+ca)

Answer 2

The above identity(given by u ) is not correct.(Since in the L.H.S c is not present whereas in the R.H.S side it is present.)
The real identities are
(a+b)²=a²+2ab+b² and
(a+b+c)²=a²+b²+c²+2(ab+bc+ca)
Suppose there is a square of area a²m²
And Let each side be increased by b m.
New area= Sum of areas of the 4 rectangles so formed
=m²((a*a)+(a*b)+(a*b)+(b*b))
=m²(a²+ab+ab+b²)
=m²(a²+2ab + b²)
HENCE VERIFIED.