Factorize following expression

Question

u^4 + u^2 x v^2 + v^4

Update:

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

I don't understand!!!!

Answer 1

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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.