This solution is shorter :

\(10x\left(x-y\right)+8y\left(y-x\right)=10x\left(x-y\right)-8y\left(x-y\right)\)

\(=\left(10x-8y\right)\left(x-y\right)=2\left(5x-4y\right)\left(x-y\right)\)

10x(x - y) + 8y(y - x)

= 10x² - 10xy + 8y² - 8xy

= 10x² - 18xy + 8y²

= 2.(5x² - 9xy + 4y²)

= 2.(4x² + x² - 2.2x.2y - xy + 4y²)

= 2.[(4x² - 2.2x.2y + 4y²) + x² - xy]

= 2.[ (2x - 2y)²  + x(x - y)]

= 2.[ 4.(x - y)² + x(x - y)]

= 2.(x - y).[4.(x - y) + x]

= 2.(x - y).[5x - y]