`a, (6x - 2)^2 + (2 - 5x)^2 + 2(6x - 2) (2 - 5x)`
`=(6x-2+2-5x)^2=x^2`
`b, (2a^2 + 2a + 1) (2a^2 - 2a + 1) - (2a^2 + 1)^2`
`=(2a^2+1)^2-4a^2 - (2a^2 + 1)^2=-4a^2`
`c,(x + 3) (x^2 - 3x + 9) - (54 + x^3)`
`=x^3+27-54-x^3=-27`
`d,(2x + y) (4x^2 - 2xy + y^2) - (2x - y) (4x^2 + 2xy + y^2)`
`=8x^3+y^3-8x^3+y^3=2y^3`
`e,(a + b)^2 - (a - b)^2`
`=(a+b-a+b)(a+b+a-b)=2b.2a=4ab`
`f,(a + b)^3 - (a - b)^3 - 2b^3`
`=(a+b-a+b)[(a+b)^2+(a+b)(a-b)+(a-b)^2]-2b^3`
`=2b.(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2)-2b^3`
`=2b.(3a^2+b^2)-2b^3=6a^2b+2b^3-2b^3`
`=6a^2b`