`a) (x - 3)(x + 7) - (x + 5)(x - 1)`
`= x^2 + 7x - 3x - 21 - (x^2 - x + 5x - 5)`
`= x^2 + 7x - 3x - 21 - x^2 + x - 5x + 5`
`= -16`
`b) (x + 8)^2 - 2(x + 8)(x - 2) + (x - 2)^2`
`= (x + 8 - x + 2)²`
`= 10^2`
`= 100`
`c) x^2(x - 4)(x + 4) - (x^2 + 1)(x^2 - 1)`
`= x²(x^2 - 16) - (x^4 - 1)`
`= x^4 - 16x^2 - x^4 + 1`
`= 1 - 16x^2`
`d) (x + 1)(x^2 - x + 1) - (x - 1)(x^2 + x + 1)`
`= x^3 + 1^3 - x^3 + 1^3`
`= 2`
`e) (x + 2)(x^2 + 2x + 4) - x(x^2 + 3)`
`= x^3 + 8 - x^3 - 3x`
`= 8 - 3x`
`f) (x - y)^2 - 2.(y - z)(y - x) + (y - z)²`
`= (x - y)² + 2(y - z)(x - y) + (y - z)²`
`= (x - y + y - z)²`
`= (x - z)²`
