Binomial Expansion

What you'll learn

Expanding \((a+b)^n\) for a positive integer \(n\) using \(\binom{n}{r}\), and finding a specific term or coefficient without expanding fully.

• \(\binom{n}{r}\) counts a choice, and it's the coefficient engine of the expansion
• The general term formula finds any term without expanding everything
• The coefficients are symmetric: \(\binom{n}{0} = \binom{n}{n} = 1\)
• A negative second term makes the signs alternate
• To find a specific coefficient, match the power of \(x\) to the right \(r\), then substitute
• A term "independent of \(x\)" is the one whose total power of \(x\) is zero
• Finding a coefficient in a product of two expansions means pairing up powers that add to the target