álgebra: exponent directe cuadrat

a^{2}+b^{2} = (1/2)( (a+b)^{2}+(a+(-b))^{2} )


1+4 = 5 = (1/2)( ( 1+2 )^{2}+( 2+(-1) )^{2} )
4+4 = 8 = (1/2)( ( 2+2 )^{2}+( 2+(-2) )^{2} )


1+9 = 10 = (1/2)( ( 1+3 )^{2}+( 3+(-1) )^{2} )
4+9 = 13 = (1/2)( ( 2+3 )^{2}+( 3+(-2) )^{2} )
9+9 = 18 = (1/2)( ( 3+3 )^{2}+( 3+(-3) )^{2} )


1+16 = 17 = (1/2)( ( 1+4 )^{2}+( 4+(-1) )^{2} )
4+16 = 20 = (1/2)( ( 2+4 )^{2}+( 4+(-2) )^{2} )
9+16 = 25 = (1/2)( ( 3+4 )^{2}+( 4+(-3) )^{2} )
16+16 = 32 = (1/2)( ( 4+4 )^{2}+( 4+(-4) )^{2} )