4x²-4x-y²+4y-3分解因式分组分解x²+4xy+4y²-2x-4y-3配方法：x²-4x-1179x²-12xy-621y²添项拆项：x^4+x^2+1x^3-11x-206题,越多越好,快

Question

4x²-4x-y²+4y-3分解因式分组分解
x²+4xy+4y²-2x-4y-3 配方法：x²-4x-117 9x²-12xy-621y² 添项拆项：x^4+x^2+1 x^3-11x-20
6题,越多越好,快

Answer 1

4x²-4x-y²+4y-3
=（4x²-4x+1)-(y²-4y+4)
=(2x-1)²-(y-2)²
=[(2x-1)+(y-2)][(2x-1)-(y-2)]
=(2x-1+y-2)(2x-1-y+2)
=(2x+y-3)(2x-y+1)
x²-4x-117
=(x²-4x+4)-121
=(x-2)²-11²
=(x-2+11)(x-2-11)
=(x+9)(x-13)
9x²-12xy-621y²
=(9x²-12xy+4y²)-625y²
=(3x-2y)²-(25y)²
=(3x-2y+25y)(3x-2y-25y)
=(3x+23y)(3x-27y)
x^4+x^2+1
=x^4+2x²+1-x²
=(x²+1)²-x²
=(x²+1+x)(x²+1-x)
x^3-11x-20
=x³-2x²-8x+2x²-3x-20
=x(x²-2x-8)+(2x+5)(x-4)
=x(x-4)(x+2)+(2x+5)(x-4)
=(x-4)[x(x+2)+(2x+5)]
=(x-4)(x²+2x+2x+5)
=(x-4)(x²+4x+5)