B) 2x²+xy-6y²=2x²+4xy-3xy-6y²=2x(x+2y)-3y(x+2y)=(x+2y)(2x-3y).
a) 2y²+my²+6y²+3my-20y-10m=y²(2y-m)+3y(2y-m)-10(2y-m)=(2y-m)(y²+3y-10)=
=(2y-m)(y²+5y-2y-10)=(2y-m)((y(y+5)-2(y+5))=(2y-m)((y+5)(y-2).
c) (18ay²+39ay-15a)/(24ay²+42ay-45a)=3a(6y²+13y-5)/((3a(8y²+14y-15))=
(6y²+13y-5)/(8y²+14y-15).
6y²+13y-5=0 D=289 y₁=-2,5 y₂=1/3 ⇒ 6y²+13y-5=(y+2,5)(y-1/3)
8y²+14y-15=0 D=676 y₁=-2,5 y₂=3/4 ⇒ 8y²+14y -15=(y+2,5)(y-3/4) ⇒
6*(y+2,5)(y-1/3)/(8*(y+2,5)(y-3/4))=3*(y-1/3)/(4*(y-3/4))=(3y-1)/(4y-3).