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F.2 Maths

知識就是力量

2008-04-16 12:54 am

Factorize 8(a^2 - a)^3 + 42(a^2 - a)^2 - 36a^2 + 36a

更新1:

To toyszchun: why there is (a - 36) ?

更新2:

To samlhy23486 you miss one step

更新3:

兩位答案都好相似交由網友幫你們select吧

回答 (1)

toyszchun

2008-04-16 1:09 am

✔ 最佳答案

8(a2 - a)3 + 42(a2 - a)2 - 36a2 + 36a
=8(a2 - a)3 + 42(a2 - a)2 - 36(a2 - 36a)
=2(a2 - 36a)[4(a2 - a)2 + 21(a2 - a) - 18]
=2(a2 - 36a)[4(a2 - a) - 3][(a2 - a) + 6]
=2a(a - 36)(4a2 - 4a - 3)(a2 - a + 6)
=2a(a - 36)(2a - 3)(2a + 1)(a - 3)(a + 2)

2008-04-16 18:34:13 補充：
對不起,我漏了

8(a² - a)³ + 42(a² - a)² - 36a² + 36a

=8(a² - a)³ + 42(a² - a)² - 36(a² - 36a)

=2(a² - 36a)[4(a² - a)² + 21(a² - a) - 18]

=2(a² - 36a)[4(a² - a) - 3][(a² - a) + 6]

=2a(a² - 36)(4a2² - 4a - 3)(a² - a + 6)

=2a(a² - 36)(2a - 3)(2a + 1)(a - 3)(a + 2)

=2a(a - 6)(a + 6)(2a - 3)(2a + 1)(a - 3)(a + 2)

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