Question

Answer 1

\(\left(x^2+\dfrac{1}{3}x+\dfrac{1}{9}\right)\left(x-\dfrac{1}{3}\right)-\left(x-\dfrac{1}{3}\right)^3\)

\(=x^3-\dfrac{1}{27}-x^3+x^2-\dfrac{1}{9}x+\dfrac{1}{27}=x^2-\dfrac{1}{9}x\)

Answer 2

\(=\left(x-\dfrac{1}{3}\right)\left(x^2+\dfrac{1}{3}x+\dfrac{1}{9}-x^2+\dfrac{2}{3}x-\dfrac{1}{9}\right)\\ =\left(x-\dfrac{1}{3}\right)x\)

Answer 3

\(=x^3-\dfrac{1}{27}-x^3+x^2-\dfrac{1}{9}x+\dfrac{1}{27}=x^2-\dfrac{1}{9}x\)