a²+b²+c²+ab+bc+ac
=1/2(2a²+2b²+2c²+2ab+2bc+2ac)
=1/2[(a²+2ab+b²)+(b²+2bc+c²)+(a²+2ac+c²)]
=1/2[(a+b)²+(b+c)²+(a+c)²]
=1/2(a+b)²+1/2(b+c)²+1/2(a+c)²
a²+b²+c²+ab+bc+ac
=1/2(2a²+2b²+2c²+2ab+2bc+2ac)
=1/2[(a²+2ab+b²)+(b²+2bc+c²)+(a²+2ac+c²)]
=1/2[(a+b)²+(b+c)²+(a+c)²]
=1/2(a+b)²+1/2(b+c)²+1/2(a+c)²