计算:①2m²-m(2m-5n)-n(5m-n)②(3x-y)²-(3x+y)²-2xy③

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  • ①2m²-m(2m-5n)-n(5m-n)

    =2m²-2m²+5mn-5mn+n²

    =n²

    .

    ②(3x-y)²-(3x+y)²-2xy

    =9x²-6xy+y²-(9x²+6xy+y²)-2xy

    =-6xy-6xy-2xy

    =-14xy

    .

    ③(m+1)(m+2)(m-1)(m-2)

    =(m+1)(m-1)(m+2)(m-2)

    =(m²-1)(m²-4)

    =m的4次幂 - 5m² +4

    .

    ④(x+1)²(x²+1)²(x-1)²

    =(x+1)²(x-1)²(x²+1)²

    =(x²-1)²(x²+1)²

    = (x的4次幂-1)²

    =x的8次幂 - 2*x的4次幂 +1

    .

    因式分

    ① 3分之4x²y³-9分之2x³y

    =9分之2*x²y*(6y²- x²)

    =9分之2*x²y*(根号6*y +x) (根号6*y -x)

    .

    ②(x²+4)²-16x²

    =[(x²+4)+4x]²[(x²+4)-4x]²

    =(x²+4x+4)²(x²-4x+4)²

    =(x+2)的4次幂*(x-2)的4次幂

    .

    ③16x的四次方-8x²y²+y的四次方

    =(4x²-y²)²

    =(2x+y)²(2x-y)²

    .

    ④-5a³+5a=-5a(a²-1)=-5a(a+1)(a-1)