Question

Answer 1

a) \(\dfrac{5\left(x-y\right)^4-3\left(x-y\right)^3+4\left(x-y\right)^2}{\left(y-x\right)^2}\)

\(=\dfrac{\left(x-y\right)^2\cdot\left[5\left(x-y\right)^2-3\left(x-y\right)+4\right]}{\left(x-y\right)^2}\)

\(=5\left(x-y\right)^2-3\left(x-y\right)+4\)

\(=5\left(x^2-2xy+y^2\right)-3\left(x-y\right)+4\)

\(=5x^2-10xy+5y^2-3x+3y+4\)

Answer 2

\(=\dfrac{5\left(x-y\right)^4-3\left(x-y\right)^3+4\left(x-y\right)^2}{\left(x-y\right)^2}\)

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