Question

simplify$(a+b+c)^{2}-(a-b-c)^{2}$

Answer 1

(a+b+c)² - (a - b - c)²

= (a² + b² + c² + 2ab + 2bc + 2ca) - [(a)²+(-b)²+(-c)²+2(a)(-b)+2(-b)(-c)+2(-c)(a)]

= a² + b² + c² + 2ab + 2bc + 2ca - (a² +b² + c² - 2ab + 2bc - 2ca

= a² + b² + c² + 2ab + 2bc + 2ca - a² - b² - c² + 2ab - 2bc + 2ca

= a² - a² + b² - b² + c² - c² + 2ab + 2ab + 2bc - 2bc + 2ca + 2ca

= 4ab + 4ca

= 4a(b + c).