9/16x2+xy2+4/9y2

Question

Solve it by mid term break method

Answer 1

(9/16)x^2+xy^2+(4/9)y^2=(9/16)(x^2+(16/9)xy^2+(16/9)(4/9)y^2)=

(9/16)(x^2+(16/9)xy^2+(64/81)y^2).

If the middle term is xy^2 then it can be combined with the last term: (9/16)(x^2+(16/9)y^2(x+4/9)).

If the middle term was meant to be xy then we have: (3x/4)^2+xy+(2y/3)^2=(3x/4+2y/3)^2 because 2(3x/4)(2y/3)=xy (the expansion of (A+B)^2=A^2+2AB+B^2. Put A=3x/4 and B=2y/3 and 2AB=xy.)

It seems likely that the middle term was supposed to be xy, not xy^2, to test your ability to spot the perfect square.