数学分解因式之十字相乘法和分组分解法要过程

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  • 分组分解法a^2-4b^2+12bc-9c^2

    =a²-(2b-3c)²

    =(a+2b-3c)(a-2b+3c)

    十字相乘法1).4x^2+30x+14

    =2(2x²+15x+7)

    =2(2x+1)(x+7)

    2).3x^2-8x+4

    =(3x-2)(x-2)

    3).5x^2y^2+23xy-10

    =(5xy-2)(xy-5)

    4).4x^2y^2-5x y^2-9y^2

    =y²(4x²-5x-9)

    =y²(4x-9)(x+1)

    分组分解法1).x^2-xy+3y-3x

    =x(x-y)-3(x-y)

    =(x-y)(x-3)

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

    =(3x+1)²-3(3x+1)

    =(3x+1)(3x+1-3)

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

    3).a^2+2ab+b^2-x^2-2xy-y^2

    =(a+b)²-(x+y)²

    =(a+b+x+y)(a+b-x-y)

    4).2y^2-5xy+2x^2-ax+2ay

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

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

    已知x+y=0.5,x+3y=1.2,求3x^2+12xy+9y^2

    原式=3(x²+4xy+3y²)

    =3(x+y)(x+3y)

    =3×0.5×1.2

    =1.8

    已知xy=-5,a-b=6,求a^2xy+b^2xy-2abxy

    原式=xy(a²-2ab+b²)

    =xy(a-b)²

    =-5×6²

    =-180