To expand the logarithmic function ln[(x^2+1)(x-1)], the initial correct step is to separate it into ln(x^2+1) + ln(x-1). However, the subsequent attempt to further break down ln(x^2+1) into ln(x^2) + ln(1) is incorrect, as ln(1) equals zero and does not contribute to the expansion. The discussion highlights that x^2 + 1 cannot be factored over the reals, which complicates further simplification without involving imaginary numbers. Ultimately, the focus remains on correctly applying logarithmic properties without missteps in factoring. Understanding these properties is crucial for accurately expanding logarithmic functions.
