The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
The general term, powers of x and missing terms
Match the requested exponent to an integer index.
Distinguish a coefficient, a term and its position.
Handle negative powers without substituting an excluded input.
For \((Ax^p+Bx^q)^n\), \(T_{r+1}=\binom nr A^{n-r}B^r x^{p(n-r)+qr}\). The index \(r\) must be an integer with \(0\le r\le n\). The fourth term uses \(r=3\). Negative powers require \(x\ne0\).