Докажите тождество 2(х+у)(x-y)+(x+y)^2+(x-y)^2=4x^2

Question

Докажите тождество 2(х+у)(x-y)+(x+y)^2+(x-y)^2=4x^2

Answer 1

2(x+y)(x-y)+(x+y)²+(x-y)²=2(x²-y²)+x²-2xy+y²+x²+2xy+y²=2x²-2y²+2x²+2y²≡4x².