(27) Explain how you can prove the difference of two cubes identity. \[ a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right) \] DONE

Step 1 ：To prove the identity \(a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\), we can expand the right side of the equation and simplify it to see if it equals to the left side of the equation.

Step 2 ：The expanded form of the right side of the equation is indeed \(a^{3} - b^{3}\), which is the same as the left side of the equation. Therefore, the identity is proven to be true.

Step 3 ：Final Answer: The identity \(a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\) is \(\boxed{true}\).