Question

a)[5(a-b)^3+2(a-b)^2]:(b-a)^2

b)5(x-2y)^3:(5x-10y)

c)(x^3+8y^3):(x+2y)

Answer 1

a) \(\frac{5\left(a-b\right)^3+2\left(a-b\right)^2}{\left(b-a\right)^2}=\frac{\left(a-b\right)^2\cdot\left[5\cdot\left(a-b\right)+2\right]}{\left(a-b\right)^2}=5\cdot\left(a-b\right)+2\)

b) \(\frac{5\left(x-2y\right)^3}{5x-10y}=\frac{5\left(x-2y\right)^3}{5\left(x-2y\right)}=\left(x-2y\right)^2\)

c) \(\frac{x^3+8y^3}{x+2y}=\frac{\left(x+2y\right)\left(x^2-2xy+4y^2\right)}{x+2y}=x^2-2xy+4y^2\)