\( \hat { i } ( 2 a - 3 b ) ^ { 3 } ( a - b ) \)

Did you know that this expression can be simplified using the Binomial Theorem? When you raise a binomial to a power, like \((2a - 3b)^3\), the expansion can be done using the theorem, which states that \((x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^{k}\). With our terms, you'll generate a series of coefficients multiplied by different powers of \(a\) and \(b\) that can be combined and simplified. To tackle expressions like this, it’s vital to keep track of your terms carefully! A common mistake is forgetting to square or cube each part correctly, especially when mixing signs. Always triple-check your calculations during expansion, ensuring that every term is accounted for – that way, you’ll avoid losing those crucial parts of the expression or making small arithmetic errors that can throw off your entire solution!