因式分解的計法 :

(a) a^2 - 6ab + 9b^2
= a^2 - 2 x a x 3b + (3b)^2 [因為3^2 = 9]
= (a - 3b)^2 [用identity (x-y)^2 = x^2 - 2xy + y^2]

(b) 運用(a)的結果,
(x+3y)^2 - 6 (x+3y) (x-y) + 9 (x-y)^2
= [x + 3y - 3 (x-y)]^2 [將(a)題目的a換做(x+3y), b換做(x-y), 甘兩條式其實係一樣的, 所以只要將(a)答案的a和b相應換走就得]
= (x + 3y - 3x + 3y)^2 [拆括號]
= (6y - 2x)^2 [將同樣有x或y的計jor佢]
= [2 (3y - x)]^2 [將公因數2抽出]
= 4 (3y - x)^2 [因為2^2 = 4]

(a)因式分解 : a^2-6ab+9b^2

because 9 = 3^2 or (-3)^2

therefore (a) is (a-3b)^2


(b)運用(a)的結果,因式分解(x+3y)^2-6(x+3y)(x-y)+9(x-y)^2

let (x+3y) = a ; (x-y) = b

get [(x+3y) - 3(x-y)] ^ 2