①化简：[x(x^3y^2)^2-2(x^2y)^3]×(-xy^2)^3

1. [x(x³y²)²-2(x²y)³]×(-xy²)³
=[x(x⁶y⁴)-2(x⁶y³)]×(-x³y⁶)
=(x⁷y⁴-2x⁶y³)×(-x³y⁶)
=-x¹⁰y¹⁰+2x⁹y⁹
= x⁹y⁹(2-xy)
2. [x²y²(x+y)²-xy²(x³+xy²)]/(1/2x²y)
=[x²y²(x²+2xy+y²)-x⁴y²- x²y⁴] /(1/2x²y)
=( x⁴y²+2 x³y³+ x²y⁴- x⁴y²- x²y⁴) /(1/2x²y)
=2 x³y³/(1/2x²y)
=4xy²
∵x=1/2,y=1;∴4xy²=4×1/2×1²=2
3. [(a+2b)(a-2b)-(2a-b)²+(3a-b)(3a-5b)]/2a
=[a²-2ab+2ab-4b²-(4a²-4ab+b²)+(9a²-15ab-3ab+5b²)]/2a
=( a²-4b²-4a²+4ab-b²+9a²-18ab+5b²)/2a
=(6a²-14ab)/2a
=3a-7b
∵a=-1,b=2;∴3a-7b=3×(-1)-7×2=-17
4. (a+b)(a-b)+2a²
=a²-b²+2a²
=3a²-b²
∵a=1,b=√2;∴3a²-b²=3-2=1