簡單數學問題兩條

x^2 - 10x - 4y2 - 12y + 16
= x^2 - 10x + 25 - 4y^2 - 12y - 9
= (x - 5)^2 - (2y + 3)^2
= (x - 5 + 2y + 3)(x - 5 - 2y - 3)
= (x + 2y - 2)(x - 2y - 8)
4x^3 - 39xy^2 + 35y^3
= 4x^3 - 4xy^2 - 35xy^2 + 35y^3
= 4x(x^2 - y^2) - 35y^2(x - y)
= 4x(x - y)(x + y) - 35y^2(x - y)
= (x - y)(4x^2 + 4xy - 35y^2)
= (x - y)(4x^2 - 10xy + 14xy - 35y^2)
= (x - y)[2x(2x - 5y) + 7y(2x - 5y)]
= (x - y)(2x + 7y)(2x - 5y)

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http://www.wolframalpha.com/input/?i=x%5E2-10x-4y2-12y%2B16
http://www.wolframalpha.com/input/?i=4x%5E3-39xy2%2B35y3+

2009-12-30 16:10:00 補充：
http://www.wolframalpha.com/input/?i=factor+4x%5E3-39xy2%2B35y3+
http://www.wolframalpha.com/input/?i=factor+x%5E2-10x-4y2-12y%2B16

x^2 - 10x - 4y2 - 12y + 16



= x^2 - 10x + 25 - 4y^2 - 12y - 9



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



= (x - 5 + 2y + 3)(x - 5 - 2y - 3)



= (x + 2y - 2)(x - 2y - 8)



4x^3 - 39xy^2 + 35y^3



= 4x^3 - 4xy^2 - 35xy^2 + 35y^3



= 4x(x^2 - y^2) - 35y^2(x - y)



= 4x(x - y)(x + y) - 35y^2(x - y)



= (x - y)(4x^2 + 4xy - 35y^2)



= (x - y)(4x^2 - 10xy + 14xy - 35y^2)



= (x - y)[2x(2x - 5y) + 7y(2x - 5y)]



= (x - y)(2x + 7y)(2x - 5y)