F.2 factorization~急~Plz

Factorize:

　-20p(3p - 2)² - 20(3p - 2)p - 5p

= -5p[ 4(3p - 2)² + 4(3p - 2) + 1 ]

= -5p[ 2²(3p - 2)² + (2)(2)(3p - 2) + 1 ]

= -5p{ [2(3p - 2)]² + (2)[2(3p - 2)] + 1 }

= -5p [2(3p - 2) + 1]²

= -5p (6p - 4 + 1)²

= -5p (6p - 3)²

= -5p [3(2p - 1)]²

= -5p [9(2p - 1)²]

= -45p(2p - 1)²

-20p(3p-2)²-20(3p-2)p-5p
=-20p(3p-2)²-20p(3p-2)-5p
=-5p[4(3p-2)²-4(3p-2)+1]
=-5p{[2(3p-2)]²-(2)[2-(3p-2)](1)+(1)²}
=-5p[2(3p-2)+1]²
=-5p(6p-4+1)²
=-5p(6p-3)²
=-5p[(9)(2p-1)]²
=-45p(2p-1)²

首先，因為你有三個數。先抽公因數(common factor)。可見公因數為-5P。

-20p(3p-2)^2-20(3p-2)p-5p

=-5p[4(3p-2)^2+4(3p-2)+1]

如果你不想混亂，可以先把(3p-2)當做y。

=-5p[4(y)^2+4(y)+1]

接下來，要分解(factorize) 4(y)^2+4(y)+1

4(y)^2+4(y)+1=(2y+1)^2

所以，

=-5p[(2y+1)^2] (中括號可寫可不寫)

希望能幫你！

以後有什麼不明白的，可以找我 ([email protected])

2014-11-10 23:42:53 補充：
沒寫完..........

y要變回(3p-2)

=-5p[(6p-3)^2]

=-5p[(3^)^2][(2p-1)^2]

=-45p(2p-1)^2

-20p(3p-2)^2-20(3p-2)p-5p
=-5p[4(36p-2)^2+4(36p-2)+1]
=-5p{[4(36p-20][36p-2+1]+1}
=-5p[(144p-8)(36p-1)+1]
=-5p(5184p-144p-288+8+1
=-5p(5040p-279)
=-5p[9(560p-31)]
=-45p(560p-31)

不知對不對，希望能幫到你=)