Упростите выражение (с+1/с) ^2-2 (m-2/m) ^2 - (m+2/m) ^2 (x/у+у/х) ^2 - (x^2/у^2 + у^2/х^2) (a+a+1/а) ^2 - (a-a+1/а) ^2

Упростим выражения.

1) (с + 1/с) ^2 - 2 = с^2 + 2c * 1/c + 1/c^2 - 2 = c^2 + 2 + 1/c^2 - 2 = c^2 + 1/c^2.

2) (m - 2/m) ^2 - (m + 2/m) ^2 = m^2 - 2m * 2/m + 4/m^2 - (m^2 + 2m * 2/m + 4/m^2) =

= m^2 - 2m * 2/m + 4/m^2 - m^2 - 2m * 2/m - 4/m^2 = - 2m * 2/m - 2m * 2/m = - 4 - 4 = - 8.

3) (x/у + у/х) ^2 - (x^2/у^2 + у^2/х^2) = x^2/y^2 + 2 * x/y * y/x + y^2/x^2 - x^2/у^2 - у^2/х^2 = 2 * x/y * y/x = 2.

4) (a + (a + 1) / а) ^2 - (a - (a + 1) / а) ^2 = a^2 + 2a * (a + 1) / a + (a + 1) ^2/a^2 - (a^2 - 2a * (a + 1) / a + (a + 1) ^2/a^2) =

= a^2 + 2a * (a + 1) / a + (a + 1) ^2/a^2 - a^2 + 2a * (a + 1) / a - (a + 1) ^2/a^2 = 2a * (a + 1) / a + 2a * (a + 1) / a =

= 2 * (a + 1) + 2 * (a + 1) = 4 * (a + 1) = 4a + 4.