Answer: [tex]\frac{(3x - 2y)(2x + 3y)}{3}[/tex]
The equation is, 2x² + (5/3)xy - 2y²
Factor out 1/3
We get, [tex]\frac{6x^{2} + 5xy - 6y^{2} }{3}[/tex]
Consider 6x² + 5xy - 6y² as a polynomial over variable x
6x² + 5yx - 6y²
Find one factor of the form [tex]kx^m+n[/tex] where [tex]kx^m[/tex] divides the monomial with the highest power 6x² and n divides the constant factor -6y².
One such factor is 2x + 3y. Factor the polynomial by dividing it by this factor.
(2x + 3y) (3x - 2y)
Rewrite the complete factored expression
[tex]\frac{(3x - 2y)(2x + 3y)}{3}[/tex]
Therefore, we get the final answer as [tex]\frac{(3x - 2y)(2x + 3y)}{3}[/tex]
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