`a) (x+y)^2 + (x-y)^2`
`= x^2 + 2xy + y^2 + x^2 - 2xy + y^2`
`= 2x^2 + 2y^2`
`b) (a-b-c)^2 - (a-b+c)^2`
`= (a - b - c - a + b - c)(a - b - c + a - b + c)`
`= -2c . 2(a-b)`
`= -4ac + 4bc`
`c) (a - x - y)^3 - ( a + x - y)^3`
`= [(a - x- y) - ( a + x - y)][(a - x - y)^2 + ( a - x - y)(a + x - y) + ( a + x - y)^2]`
`= -2x(3a^2 + x^2 + 3y^2 - 6ay)`
`= 12axy - 6a^2x - 6xy^2 - 2x^3`
`d) (1 + x + x^2)(1-x)(1+x)(1-x+x^2)`
`= ( 1 - x^3) ( 1 + x^3 )`
`= 1 - x^6`