(x-y)^3-(y-x)^25a^2(x-y)+10a(y-x)(m-n)^2-10(n-m)+25(x+y)^2 -

6个回答

  • (1)

    (x-y)^3-(y-x)^2

    =(x-y)^3-(x-y)^2 (提出公因子(x-y)^2)

    =(x-y)^2*(x-y-1)

    (2)

    5a^2(x-y)+10a(y-x)

    =5a^2(x-y)-10a(x-y) (提出公因子5a(x-y))

    =5a(x-y)(a-2)

    (3)

    (m-n)^2-10(n-m)+25

    =(m-n)^2+10(m-n)+25 (完全平方公式)

    =(m-n+5)^2

    (4)

    (x+y)^2 -2(x+y)(x-y)+(x-y)^2 (完全平方公式)

    =[(x+y)-(x-y)]^2

    =(2y)^2

    =4y^2

    (5)

    x^2 +12xy+36y^2

    =x^2+2x(6y)+(6y)^2 (完全平方公式)

    =(x+6y)^2

    (6)

    1-8xy^2+16x^2y^4

    =1-2*(4x)*y^2+(4x)^2*(y^2)^2 (完全平方公式)

    =(1-4xy^2)^2

    (7)

    x^4-8x^2+16 (完全平方公式)

    =(x^2-4)^2 (再由平方差公式)

    =[(x+2)(x-2)]^2

    =(x+2)^2*(x-2)^2

    (8)

    4(x-y)^2-4(x-y)+1

    =[2(x-y)]^2-2*2(x-y)+1 (完全平方公式)

    =[2(x-y)-1]^2

    =(2x-2y-1)^2

    (9)

    18x^3-27x^4-3x^2 (先提出公因子3x^2)

    =3x^2(6x-9x^2-1)

    =-3x^2(9x^2-6x+1) (括号内为完全平方)

    =-3x^2(3x-1)^2

    (10)

    x^4-18x^2+81 (完全平方公式)

    =(x^2-9)^2 (再由平方差公式)

    =[(x+3)(x-3)]^2

    =(x+3)^2*(x-3)^2

    (11)

    16a^2b^4-8ab^2c^2+c^4

    =(4ab^2)^2-2*(4ab^2)c^2+(c^2)^2 (完全平方公式)

    =(4ab^2-c^2)^2

    (12)

    9(2x-y)^2-6(2x-y)+1

    =[3(2x-y)]^2-6(2x-y)+1 (完全平方公式)

    =[3(2x-y)-1]^2

    =(6x-3y-1)^2