中三級數學問題，請各位高人指點

只要對identity夠熟就好易做到.
Btw the question is not well posed.

I treat it as " Factorize x^4+y^4."


Solution:
x^4+y^4
=(x^2)^2+(y^2)^2-2x^2*y^2+2x^2*^2
=(x^2+y^2)^2-2x^2*y^2
=(x^2+y^2)^2-(sqrt(2)xy)^2
=[x^2+y^2-sqrt(2)xy][x^2+y^2+sqrt(2)xy]

sqrt(2) = square root of 2

[x^2+y^2-sqrt(2)xy][x^2+y^2+sqrt(2)xy] is final ans as It cannot be further factorized.
Reason: treat y as constant, D=b^2-4ac=(sqrt(2)y)^2-4(1)(y^2)=2y^2-4y^2=-2y^2<0, thus cannot be further factorized.

Notes that factorization-type questions need you to factorize the expression until it cannot be factorized anymore.

x^4+y^4
=(x²+y²)²-(2x²y²)
=[(x+y)²-(2xy)]²-(2x²y²)

2013-10-03 19:21:45 補充：
中三級數學????
好似唔系!

同學們：

x⁴ + y⁴

= x⁴ + 2x²y² + y⁴ - 2x²y²

= (x²+y²)² - 2x²y²

= (x²+y²)² - (√2xy)²

= (x²+y²+√2xy)(x²+y²-√2xy)

2013-09-30 22:02:23 補充：
星塵，以下是一題常見題，請注意：

Factorize x⁴ + x²y² + y⁴.

Consider x⁴ + x²y² + y⁴

= x⁴ + 2x²y² + y⁴ - x²y²

= (x²+y²)² - (xy)²

= (x² + xy + y²)(x² - xy + y²)

好少做4次方......

2013-09-30 22:07:22 補充：
Thanks for your teaching.

2013-09-30 22:12:00 補充：
I'll remember it.

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

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