A-maths~~~~~~~~~

2007-07-02 5:25 am
按x的升冪序,展開下列各式至X³

(2-3x)^5 (2+3x)^5

回答 (1)

2007-07-02 5:56 am
✔ 最佳答案
(2-3x)^5 (2+3x)^5

= { ( 2 - 3x )( 2 + 3x ) }^5

= ( 4 - 9x^2 )^5

= ( 5! / 0! 5! )( 4 )^5 ( -9x^2 )^0 + ( 5! / 4! 1! )( 4 )^4 ( - 9x^2 )^1 + ( 5! / 3! 2! )( 4 )^3 ( - 9x^2 )^2 + ...

= ( 1 )( 1024 )( 1 ) + ( 5 )( 256 )( -9x^2 ) + ( 10 )( 64 )( 81x^4 ) + ...

= 1024 - 11520 x^2 + ...

If you expand them separately, you will find that the X³ will be cancelled out in the middle, so there should be no X³ in the answer.

Hope it helps.
參考: My Maths Knowledge


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