F.2 Factorization

9x²-y²+6x-2y
=[(3x)²-y²]-2(3x-y) ...... 因式分解 x^2 - y^2 = ( x + y ) ( x - y )
=(3x-y)(3x+y)+2(3x-y)
=(3x-y)[(3x+y)+2] ...... 公因數 : ( 3x - y ) , 剩餘的兩組數放於[ ] 內 , ∵ ax +bx = x ( a + b )
=(3x-y)(3x+y+2) ...... 化簡 [ ] 內的數 , 便得出 ( 3x + y + 2 )

9x²-y²+6x-2y
=(3x-y)²-2(3x-y)
[首先將9x²-y²的二次方抽出(注意:9=3²),所以應寫成(3x)²-y²=(3x-y)(3x+y)]
[不應寫成(3x-y)²,因為a²-b²=(a-b)(a+b)]
[然後6x-2y的部份,抽取公因數2,所以=2(3x-y)]
=(3x-y)(3x+y)+2(3x-y)
=(3x-y)[(3x+y)+2]
[之後將(3x-y)(3x+y)+2(3x-y),抽取公因數(3x-y),所以=(3x-y)[(3x+y)+2]]
=(3x-y)(3x+y+2)


希望幫到你!!

佢個方法....好怪...我自己寫一次，好簡單的
先要知x²-y²=(x+y)(x-y)
9x²-y²+6x-2y
=(3x+y)(3x-y)+2(3x-y)<---抽3x-y出黎
=(3x-y)(3x+y+2)

=(3x-y)²-2(3x-y)<----佢呢度已經錯左
呢個(3x-y)²唔等於(3x-y)(3x+y)
但佢又計到個answer先勁....