Упростить выражение 3x (x+y+c) - 3y (x-у-c) - 3c (x+y-c)

3 ⋅ x ⋅ (x + y + c) - 3 ⋅ y ⋅ (x - у - c) - 3 ⋅ c ⋅ (x + y - c).

Раскрываем первую скобку:

3 ⋅ x ⋅ (x + y + c) = 3 ⋅ x ⋅ x + 3 ⋅ x ⋅ y + 3 ⋅ x ⋅ c = 3 x² + 3 x y + 3 x c.

Раскрываем вторую скобку:

3 ⋅ y ⋅ (x - у - c) = 3 ⋅ y ⋅ x - 3 ⋅ y ⋅ у - 3 ⋅ y ⋅ c = 3 y x - 3 y² - 3 y c.

Раскрываем третью скобку:

3 ⋅ c ⋅ (x + y - c) = 3 ⋅ c ⋅ x + 3 ⋅ c ⋅ y - 3 ⋅ c ⋅ c = 3 c x + 3 c y - 3 c².

Получаем выражение:

(3 x² + 3 x y + 3 x c) - (3 y x - 3 y² - 3 y c) - (3 c x + 3 c y - 3 c²).

Раскрываем скобки, перемещаем и упрощаем:

3 x² + 3 x y + 3 x c - 3 y x + 3 y² + 3 y c - 3 c x - 3 c y + 3 c² = 3 x² + 3 y² + 3 c² + 3 x y - 3 y x + 3 x c - 3 c x + 3 y c - 3 c y = 3 x² + 3 y² + 3 c².