4y.(3y - 5z) - 3z(5z - 3y)
= 4y ( 3y - 5z ) - 3z .[ - ( 3y - 5z ) ]
= 4y ( 3y - 5z ) + 3z ( 3y - 5z )
= ( 3y - 5z ) ( 4y + 3z )
Study well
\(4y\left(3y-5z\right)-3z\left(5z-3y\right)=\left(...\right)\left(4y+3z\right)\)
\(\Rightarrow4y\left(3y-5z\right)+3z\left(3y-5z\right)=\left(...\right)\left(4y+3z\right)\)
\(\Rightarrow\left(4y+3z\right)\left(3y-5z\right)=\left(...\right)4y-3z\)
\(\Rightarrow\left(...\right)=3y-5z\)