因式分解GE題目~

1. a^2 -9a(b-c)+ 20(b-c)^2 =?

Let (b-c) be u (It's easier to see)
a^2-9au+20u^2
a -5u
x
a -4u
-------
-5au-4au=-9au
.'.(a-5u)(a-4u)
=[a-5(b-c)][a-4(b-c)]
個u係比你易d明,果d step可以唔洗寫
=(a-5b+5c)(a-4b+5c)

2. 18-2x^3=?
抽個２出黎先
=2( 9-x^3 )
=2( 3^3-x^3)
=2(3-x)(3^2+3x+x^2)
=2(3-x)(9+3x+x^2)

3. a^3+b^3-a-b=?
計左a^3+b^3先
=(a+b)(a^2-ab+b^2) -a-b
=(a+b)(a^2-ab+b^2) -(a+b)
==(a+b)(a^2-ab+b^2 -1)

P.S.通常叫你計因式分解都係要你最後個答案剩番成同除
就好似(........)(........)(......)咁
除都okay
唔好見到 ...+...-...咁就okay

a^2 -9a(b-c) 20(b-c)^2
=a^2-4a(b-c)-5a(b-c) 20(b-c)^2
=[a^2-4a(b-c)]-[5a(b-c)-20(b-c)^2]
=a[a-4(b-c)]-5(b-c)[a-4(b-c)]
=[a-4(b-c)][a-5(b-c)]
=(a-4b+4c)(a-5b+5c)
呢題係咪好special..唔使靠撞彩(唔係一般的十字相乘)
18-2x^3
=2(9-x^3) (頂多做到咁)
因不是立方數,不能因式分解
a^3+ b^3-a-b
=a^3 + b^3 - (a + b)
= (a + b)(a^2 -ab + b^2) - (a + b)
= (a + b) (a^2 - ab + b^2 - 1)