Question

(a + b - c)^2 - (a - b + c)^2​

Answer 1

Step-by-step explanation:

(a+b+c)^2 = a^2 +b^2 +c^2 +2ab+2bc+2ac

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

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

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

=a^2+b^2-c^2 + 2ab-2bc-2ac - a^2 +b^2 - c^2+2ab+2bc-2ac

= 2b^2-2c^2+2ab - 2ac

= 2b^2+2ab-2c^2-2ac

=2b(b+a)-2c(c+a)