Factorize following expression

2009-11-10 12:26 am
u^4 + u^2 x v^2 + v^4
更新1:

u^4 + 2(u^2) (v^2) + v^4 - (u^2)(v^2) I don't understand!!!!

回答 (1)

2009-11-10 12:29 am
✔ 最佳答案
u^4 + u^2 x v^2 + v^4

= u^4 + 2(u^2) (v^2) + v^4 - (u^2)(v^2)

= (u^2 + v^2)^2 - (uv)^2

= (u^2 + v^2 + uv)(u^2 + v^2 - uv)


2009-11-09 17:09:46 補充:
u^4 + u^2 x v^2 + v^4

= u^4 + (u^2) (v^2) + v^4 + (u^2)(v^2) - (u^2)(v^2)

= u^4 + (u^2)(v^2) + (u^2)(v^2) + v^4 - (u^2)(v^2)

= u^4 + 2(u^2) (v^2) + v^4 - (u^2)(v^2)

that means + (u^2)(v^2) first and - (u^2)(v^2) the value have no change.


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