Question

Calcule:
a) (a+b+c)² - (a²+ b² + c²)

b) (a+b)² - (b+c)² - (a+c) (a-c)

Answer 1

$a) \\ (a+b+c)^2=(a+b+c)(a+b+c) =\\ \\ =a(a+b+c)+b(a+b+c)+c(a+b+c)= \\ \\ a^2+ab+ac+ba+b^2+bc+ca+cb+c^2 = \\ \\= a^2+b^2+c^2+2ab+2bc+2ac\\ \\ \\ (a+b+c)^2-(a^2+b^2+c^2)= \\ \\ =a^2+b^2+c^2+2ab+2bc+2ac-a^2-b^2-c^2= \\ \\ =2ab+2bc+2ac$

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