作业帮分解因式（x^2+3x+2)(3+8x+4x^2)-90xy(xy+1)+(xy+3)-2(x+y+0.5)-(x+y-1)^2
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/16 05:34:34
分解因式（x^2+3x+2)(3+8x+4x^2)-90xy(xy+1)+(xy+3)-2(x+y+0.5)-(x+y-1)^2
分解因式
（x^2+3x+2)(3+8x+4x^2)-90
xy(xy+1)+(xy+3)-2(x+y+0.5)-(x+y-1)^2
分解因式（x^2+3x+2)(3+8x+4x^2)-90xy(xy+1)+(xy+3)-2(x+y+0.5)-(x+y-1)^2
（x^2+3x+2)(3+8x+4x^2)-90
=（x+2）（x+1）（2x+1）（2x+3）-90
=（x+2）（2x+1）（x+1）（2x+3）-90
=（2x^2+5x+2）(2x^2+5x+3)-90
=(2x^2+5x)^2+5(2x^2+5x)+6-90
=(2x^2+5x)^2+5(2x^2+5x)-84
=(2x^2+5x-7)(2x^2+5x+12)
=(2x+7)(x-1)(2x^2+5x+12)
xy(xy+1)+(xy+3)-2(x+y+0.5)-(x+y-1)^2
=xy(xy+1)+(xy+1)+2-2(x+y)-1-[(x+y)^2-2(x+y)+1]
=(xy+1)^2+2-2(x+y)-1-(x+y)^2+2(x+y)-1
=(xy+1)^2-(x+y)^2
=(xy+x+y+1)(xy-x-y+1)
=(x+1)(y+1)(x-1)(y-1)
（x^2+3x+2)(3+8x+4x^2)-90
=(x+1)(x+2)(2x+3)(2x+1)-90
=[(x+1)(2x+3)][(x+2)(2x+1)]-90
=(2x^2+5x+3)(2x^2+5x+2)-90 (把2x^2+5x当作一个整体)
=(2x^2+5x)^2+5(2x^2+5x)-84
=(2x^2+5x+12)(2x^2+5x-7...
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（x^2+3x+2)(3+8x+4x^2)-90
=(x+1)(x+2)(2x+3)(2x+1)-90
=[(x+1)(2x+3)][(x+2)(2x+1)]-90
=(2x^2+5x+3)(2x^2+5x+2)-90 (把2x^2+5x当作一个整体)
=(2x^2+5x)^2+5(2x^2+5x)-84
=(2x^2+5x+12)(2x^2+5x-7)
=(2x^2+5x+12)(x-1)(2x+7)
xy(xy+1)+(xy+3)-2(x+y+0.5)-(x+y-1)^2
=(xy)^2+xy+xy+3-2(x+y-1)-3-(x+y-1)^2+1-1(注意常数项的添加)
=[(xy)^2+2xy+1]-[1+2(x+y-1)+(x+y-1)^2]
=(xy+1)^2-(x+y-1+1)^2
=(xy+1)^2-(x+y)^2
=(xy+1-x-y)(xy+1+x+y)
=(x-1)(y-1)(x+1)(y+1)
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