`a)`
`(x+5)^2-2(x+3)(x-3)-(x-2)^2`
`=(x^2+10x+25)-2(x^2-9)-(x^2-4x+4)`
`=x^2+10x+25-2x^2+18-x^2+4x-4`
`=(x^2-2x^2-x^2)+(10x+4x)+(25+18-4)`
`=-2x^2+14x+39`
`b)`
`(x+2y)(x-2y)-(x+y)^2`
`=x^2-(2y)^2-(x^2+2xy+y^2)`
`=x^2-4y^2-x^2-2xy-y^2`
`=(x^2-x^2)-(4y^2+y^2)-2xy`
`=-5y^2-2xy`
`c)`
`(2x+1)^2-(3x-2)^2`
`=(2x+1+3x-2)(2x+1-3x+2)`
`=(5x-1)(3-x)`
`=-5x^2+16x-3`
`d)`
`4(x+1)^2-(2x-1)^2`
`=[2(x+1)]^2-(2x-1)^2`
`=(2x+2)^2-(2x-1)^2`
`=(2x+2-2x+1)(2x+2+2x-1)`
`=3(4x+1)`
`=12x+3`