①化简：[x(x^3y^2)^2-2(x^2y)^3]×(-xy^2)^3

题目

①化简：[x(x^3y^2)^2-2(x^2y)^3]×(-xy^2)^3
②先化简再求值：[x^2y^2(x+y)^2-xy^2(x^3+xy^2)]/(1/2x^2y),其中x=1/2,y=1
③先化简再求值：[(a+2b)(a-2b)-(2a-b)^2+(3a-b)(3a-5b)]/2a,其中a=-1,b=2
④先化简再求值：(a+b)(a-b)+2a^2,其中a=1,b=根号2

答案

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