(ax+by) ^2 +(bx- au) ^2
sol={a^x^2+b^2 y^2+ 2abxy+ b^2x^2+a^2y^2-2abxy}
=a^2x^2 +b^2 y^2+ b^2x^2+a^2y^2
=a^2x^2 +b^2 x^2+a^2y^2+b^2y^2
= x^2(a^2+b^2) +y^2(a^2+b^2)
=( a^2+b^2) (x^2+y^2)
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