The expressions you've provided can be factored as follows:
For the expression \(a^2 - ab + b^2\), this is not factorable over the reals into linear factors since it doesn't have real roots (it can be factored in complex numbers, but that usually goes beyond elementary algebra). However, it can be expressed in a different way: \[ a^2 - ab + b^2 = \left(a - \frac{b}{2}\right)^2 + \frac{3b^2}{4} \]
The expression \(a^3 + b^3\) can be factored using the sum of cubes formula: \[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]
If you have specific questions about these expressions or need further assistance with algebra, feel free to ask!
