$2 (2 x^{2} - 3 y^{2}) (5 x^{2} + 2 x y - 3 y^{2})$

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Solution

$2 (2 x^{2} - 3 y^{2}) (5 x^{2} + 2 x y - 3 y^{2})$
$2 (2 x^{2} - 3 y^{2}) (5 x^{2} + 2 x y - 3 y^{2}) = 2 (2 x^{2} - 3 y^{2}) (5 x^{2} + 5 x y - 3 x y - 3 y^{2}) = 2 (2 x^{2} - 3 y^{2}) (5 x (x + y) - 3 y (x + y))) = 2 (2 x^{2} - 3 y^{2}) (5 x - 3 y) (x + y) = 2 (\sqrt{2} x - \sqrt{3} y) (\sqrt{2} x + \sqrt{3} y) (5 x - 3 y) (x + y)$

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Q. What should be added to

2 x^{2} - 3 y^{2}

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2(2x2−3y2)(5x2+2xy−3y2)

2(2x2−3y2)(5x2+2xy−3y2) 2(2x2−3y2)(5x2+2xy−3y2)=2(2x2−3y2)(5x2+5xy−3xy−3y2)=2(2x2−3y2)(5x(x+y)−3y(x+y)))=2(2x2−3y2)(5x−3y)(x+y)=2(√2x−√3y)(√2x+√3y)(5x−3y)(x+y)

$2 (2 x^{2} - 3 y^{2}) (5 x^{2} + 2 x y - 3 y^{2})$