`a)2x(2x-1)²-3x(x+3)(x-3)-4x(x+1)²`
`=2x(4x²-4x+1)-3x(x²-9)-4x(x²+2x+1)`
`=8x³-8x²+2x-3x³+27x-4x³-8x²-4x`
`=(8x³-3x³-4x³)+(-8x²-8x²)+(2x+27x-4x)`
`=x³-16x²+25x`
`b)(a-b+c)²-(b-c)²+2ab-2ac`
`=(a-b+c+b-c)(a-b+c-b+c)+2ab-2ac`
`=a(a-2b+2c)+2ab-ac`
`=a²-2ab+2ac+2ab-2ac`
`=a²+(-2ab+2ab)+(2ac-2ac)`
`=a²`
`c)(3x+1)²-2(3x+1)(3x+5)+(3x+5)²`
`=[(3x+1)-(3x+5)]²`
`=(3x+1-3x-5)²`
`=(-4)²`
`=16`
`d)4(3²+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)`
`=[8(3²+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)]/2`
`=[(3^2-1)(3²+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)]/2`
`=[[(3^2)^2-1^2](3^4+1)(3^8+1)(3^16+1)(3^32+1)]/2`
`=[(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)]/2`
`=[[(3^4)^2-1^2](3^8+1)(3^16+1)(3^32+1)]/2`
`=[(3^8-1)(3^8+1)(3^16+1)(3^32+1)]/2`
`=[[(3^8)^2-1^2](3^16+1)(3^32+1)]/2`
`=[(3^16-1)(3^16+1)(3^32+1)]/2`
`=[[(3^16)^2-1^2](3^32+1)]/2`
`=[(3^32-1)(3^32+1)]/2`
`=[(3^32)^2-1^2]/2`
`=(3^64-1)/2`
