Vereinfache mit Hilfe der binomischen Formeln: (a+b+c)(-a+b+c)+(2c+b-a)²-2(b+c)²

Question

(a+b+c)(-a+b+c)+(2c+b-a)²-2(b+c)²

Answer 1

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

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

(-a^2 + ab + ac - ab + b^2 + bc - ac + bc + c^2) + (4c^2 + 2bc - 2ac + 2bc + b^2 - ab - 2ac - ab + a^2) - 2(b^2 + 2bc + c^2)

(-a^2 + b^2 + 2bc + c^2) + (4c^2 + 4bc - 4ac + b^2 - 2ab + a^2) - 2(b^2 + 2bc + c^2)

-a^2 + b^2 + 2bc + c^2 + 4c^2 + 4bc - 4ac + b^2 - 2ab + a^2 - 2b^2 - 4bc - 2c^2

3c^2 + 2bc - 4ac - 2ab