Question

Докажите тождество: (а+b-c)^2=a^2+b^2+c^2+2ab-2bc-2ac

Answer 1

$(a+b-c)^2=(a+b-c)(a+b-c)=(a+b-c)\cdot a + (a+b-c)\cdot b + \\ + (a+b-c)\cdot (-c) = a^2+ab-ac+ab+b^2-bc-ac-bc+c^2 = \\ =a^2+b^2+c^2+2ab-2ac-2bc \\ \\ a^2+b^2+c^2+2ab-2bc-2ac = a^2+b^2+c^2+2ab-2ac-2bc$