Đáp án:
$5x^2-2xy+3y^2$
Giải thích các bước giải:
$(13x^2y^2-5x^4+6y^4-13x^3y-13xy^3):(2y^2-x^2-3xy)\\
=(-5x^4-13x^3y+13x^2y^2-13xy^3+6y^4):(2y^2-x^2-3xy)\\
=(-5x^4-15x^3y+2x^3y+10x^2+y^2+6x^2y^2-3x^2y^2-4xy^3-9xy^3+6y^4):(2y^2-x^2-3xy)\\
=\left [ (-5x^4-15x^3y+10x^2y^2)+(2x^3y+6x^2y^2-4xy^3)+(-3x^2y^2-9xy^3+6y^4) \right ]:(2y^2-x^2-3xy)\\
=\left [ -5x^2(x^2+3xy-2y^2)+2xy(x^2+3xy-2y^2)-3y^2(x^2+3xy-2y^2) \right ]:(2y^2-x^2-3xy)\\
=\left [ (x^2+3xy-2y^2)(-5x^2+2xy-3y^2)\right ]:\left [-(-2y^2+x^2+3xy) \right ]\\
=-(-5x^2+2xy-3y^2)\\
=5x^2-2xy+3y^2$
