因式分解的計法

1) (a)因式分解x^3-x^2y+xy^2
=x(x^2-xy+y^2)

(b)因式分解yx^2-xy^2+y^3
=y(x^2-xy+y^2)

(c) 因式分解x^3+y^3
(a)+(b):
x^3-x^2y+xy^2+yx^2-xy^2+y^3=x(x^2-xy+y^2)+y(x^2-xy+y^2)
x^3+y^3=(x+y)(x^2-xy+y^2)

2 (a) 因式分解 9x^2+12xy+4y^2
=(3x+2y)^2

(b) 運用(a)的結果,因式分解9x^2+12xy-21y^3
=9x^2+12xy+4y^2-25y^2
=(3x+2y)^2-(5y)^2
=(3x+2y+5y)(3x+2y-5y)
=(3x+7y)(3x-3y)
=3(x-y)(3x+7y)

*****~~-21y^3--- >-21y^2, 這裏打錯了吧!