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x^{2}+2xy-3x-2yx-4y^{2}+6y+3x+6y-9
Apply the distributive property by multiplying each term of x-2y+3 by each term of x+2y-3.
x^{2}-3x-4y^{2}+6y+3x+6y-9
Combine 2xy and -2yx to get 0.
x^{2}-4y^{2}+6y+6y-9
Combine -3x and 3x to get 0.
x^{2}-4y^{2}+12y-9
Combine 6y and 6y to get 12y.
x^{2}+2xy-3x-2yx-4y^{2}+6y+3x+6y-9
Apply the distributive property by multiplying each term of x-2y+3 by each term of x+2y-3.
x^{2}-3x-4y^{2}+6y+3x+6y-9
Combine 2xy and -2yx to get 0.
x^{2}-4y^{2}+6y+6y-9
Combine -3x and 3x to get 0.
x^{2}-4y^{2}+12y-9
Combine 6y and 6y to get 12y.