UC知道两道因式分解
来源：百度知道 编辑：UC知道 时间：2024/05/24 23:40:43
(x^2-5)(x^2-5x-2)-24
现在2题的答案不对
(1)
-3x(y^2-1)+3y(x^2-1)
=-3x*y^2+3x+3x^2*y-3y
=-3x*y^2+3x^2*y-3y+3x
=-3xy(x-y)+3(x-y)
=(3-3xy)(x-y)
=3(x-y)(1-xy)
(2)
(x^2-5)(x^2-5x-2)-24
=(x^2-1-4)(x^2-5x-2)-24
=(x^2-1)(x^2-5x-2)-4(x^2-5x-2)-24
=(x^2-1)(x^2-5x-2)-4x^2+20x-16
=(x-1)(x+1)(x^2-5x-2)-4(x^2-5x+4)
=(x-1)(x^3-4x^2-7x-2)-4(x-1)(x-4)
=(x-1)[x^3-4x^2-7x-2-4(x-4)]
=(x-1)(x^3-4x^2-11x+14)
=(x-1)(x^3-x^2-3x^2+3x-14x+14)
=(x-1)[(x^3-x^2)-(3x^2-3x)-(14x-14)]
=(x-1)[x^2(x-1)-3x(x-1)-14(x-1)]
=(x-1)^2*(x^2-3x-14)
(1)
-3x(y^2-1)+3y(x^2-1)
=-3x*y^2+3x+3x^2*y-3y
=-3x*y^2+3x^2*y-3y+3x
=-3xy(x-y)+3(x-y)
=(3-3xy)(x-y)
=3(x-y)(1-xy)
(2)
(x^2-5)(x^2-5x-2)-24
=(x^2-1-4)(x^2-5x-2)-24
=(x^2-1)(x^2-5x-2)-4(x^2-5x-2)-24
=(x^2-1)(x^2-5x-2)-4x^2+20x-16
=(x-1)(x+1)(x^2-5x-2)-4(x^2-5x+4)
=(x-1)(x^3-4x^2-7x-2)-4(x-1)(x-4)
=(x-1)[x^3-4x^2-7x-2-4(x-4)]