Question 200867
9x^2 +4y^2
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very  interesting  problem.
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If  this  was ,, 9x^2 -4y^2 ,, just  factor  difference  of  squares,,,
(3x+2y)(3x-2y).  To  use  this  form  on  the  positive,  lets  rewrite  the  eqn
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(9x^2 - (-4) y^2
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(3x+sqrt(-4)y) (3x- sqrt(-4)y)
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 (3x+2iy) (3x - 2iy)
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check  using  FOIL
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F = 9x^2,,,,O= -6ixy,,,I = +6ixy ,,,,L = -4i^2 y^2 = 9x^2 +4y^2,,(i^2 = -1),,,,,ok