Question

x^2(x+1)-y(xy-x) 因式分解

求过程

Answer 1

x^2(x+1)-y(xy-x) 因式分解
= x³ + x² - xy² +xy
= x³ - xy²+ x² +xy
=x ( x²-y² ) + x (x+y)
=x ( x+y )(x-y) + x (x+y)
= (x ²+xy +x ) (x+y)
= x (x +y +1 ) (x+y)

追问

从 x ( x+y )(x-y) + x (x+y) 怎么到这一步的 ：(x ²+xy +x ) (x+y)

追答

其实可以直接到最后一步

=x ( x+y )(x-y) + x (x+y)
=x ( x+y )(x-y+1)

追问

从 x ( x+y )(x-y) + x (x+y) 到这一步呢 x ( x+y )(x-y+1)

追答

x ( x+y )(x-y) + x (x+y)
= x ( x+y ) (x-y) + x (x+y) x 1

= x ( x+y )(x-y+1)

追问

为什么要 X 1 呢

Answer 2

x^2(x+1)-y(xy-x)
=x^3+x^2 - xy^2+xy
=(x^3- xy^2)+(x^2+xy)
=x(x^2-y^2)+x(x+y)
=x(x+y)(x-y)+x(x+y)
=x(x+y)(x-y+1)

追问

从 x ( x+y )(x-y) + x (x+y) 怎么到这一步的 ：(x ²+xy +x ) (x+y)

追答

x ( x+y )是x ( x+y )(x-y)和x (x+y)的公因式

Answer 3

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

Answer 4

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

Answer 5

x(x+y)(x-y+1)