`a)`

`A = (x - 3y)^2 + (2x + 5y)^2 - (2x - y)(2x + y)`

`A = (x^2 - 6xy + 9y^2) + (4x^2 + 20xy + 25y^2) - (4x^2 - y^2)`

`A = x^2 - 6xy + 9y^2 + 4x^2 + 20xy + 25y^2 - 4x^2 + y^2`

`A = (x^2 + 4x^2 - 4x^2) + (-6xy + 20xy) + (9y^2 + 25y^2 + y^2)`

`A = x^2 + 14xy + 35y^2`

`b)`

`B = (x - 1)^3 + (3 + x)^3 - (x - 2)(x^2 + 2x + 4)`

`B = (x^3 - 3x^2 + 3x - 1) + (27 + 27x + 9x^2 + x^3) - (x^3 - 8)`

`B = x^3 - 3x^2 + 3x - 1 + x^3 + 9x^2 + 27x + 27 - x^3 + 8`

`B = (x^3 + x^3 - x^3) + (-3x^2 + 9x^2) + (3x + 27x) + (-1 + 27 + 8)`

`B = x^3 + 6x^2 + 30x + 34`

`c)`

`C = (a + b - c)^2 + (b + c - a)^2 + (c + a - b)^2 + (a + b + c)^2`

Áp dụng `(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx`:

`@ (a + b - c)^2 = a^2 + b^2 + c^2 + 2ab - 2bc - 2ca`

`@ (b + c - a)^2 = a^2 + b^2 + c^2 - 2ab + 2bc - 2ca`

`@ (c + a - b)^2 = a^2 + b^2 + c^2 - 2ab - 2bc + 2ca`

`@ (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca`

`C = 4a^2 + 4b^2 + 4c^2 + (2ab - 2ab - 2ab + 2ab) + (-2bc + 2bc - 2bc + 2bc) + (-2ca - 2ca + 2ca + 2ca)`

`C = 4a^2 + 4b^2 + 4c^2`

`C = 4(a^2 + b^2 + c^2)`