The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Finite expansions, factorial notation and signs
Expand positive integer powers accurately.
Keep constant powers, signed factors and the requested order.
Distinguish a complete identity from a truncated expression.
For a positive integer \(n\), \((a+b)^n=\sum_{r=0}^{n}\binom nr a^{n-r}b^r\), where \(\displaystyle \binom nr=\frac{n!}{r!(n-r)!}\) and \(0!=1\). Apply the exponent to the whole signed term. "First terms" are not a complete expansion.