Question

(x-2y)(y-3x)+(x+y)(x-3y)-(y-3x)(4x-5y)

Answer 1

Hello,
(x-2y)(y-3x)+(x+y)(x-3y)-(y-3x)(4x-5y);
=(xy-3x²-2y²+6xy)+(x²-3xy+xy-3y²)-(4xy-5y²-12x²+15xy);
=7xy-3x²-2y²+(x²-2xy-3y²)-(19xy-5y²-12x²);
=7xy-3x²-2y²+x²-2xy-3y²-19xy+5y²+12x²;
=(-3+1+12)x²+(7-2-19)xy+(-2-3+5)y²;
=10x²-14xy;
=2x(5x-7y)

bye :-)

Answer 2

FULL ANSWER WITH STEPS

$(x-2y)(y-3x)+(x+y)(x-3y)-(y-3x)(4x-5y)$
$= xy-3x^{2}-2y^{2}+6xy+(x+y)(x-3y)-(y-3x)(4x-5y)$
$= -3x^{2}+7xy-2y^{2}+(x+y)(x-3y)-(y-3x)(4x-5y)$
$= -3x^{2}+7xy-2y^{2}+x^{2}-3xy+xy-3y^{2}-(y-3x)(4x-5y)$
$= -3x^{2}+7xy-2y^{2}+x^{2}-2xy-3y^{2}-(y-3x)(4x-5y)$
$= -3x^{2}+7xy-2y^{2}+x^{2}-2xy-3y^{2}-(4xy-5y^{2}-12x^{2}+15xy)$
$= -3x^{2}+7xy-2y^{2}+x^{2}-2xy-3y^{2}-(-12x^{2}+19xy-5y^{2})$
$= -3x^{2}+7xy-2y^{2}+x^{2}-2xy-3y^{2}+12x^{2}-19xy+5y^{2}$
$= -3x^{2}+x^{2}+12x^{2}+7xy-2xy-19xy-2y^{2}-3y^{2}+5y^{2}$
$= (-3+1+12)x^{2}+(7-2-19)xy+(-2-3+5)y^{2}$
$= (-3+13)x^{2}+(7-21)xy+(-5+5)y^{2}$
$= 10x^{2}+(-14)xy+(0)y^{2}$
$= 10x^{2}-14xy$

Trust me. This is the correct answer. 

Hope this may help you. 

If you have any doubt, then you can ask me in the comments.