Enter n and instantly expand (x + y)ⁿ — every term, every coefficient, using Pascal’s Triangle values.
Binomial Expansion Calculator
How It’s Calculated
The Binomial Theorem states (x + y)ⁿ = Σ (nCk) x(n−k) yk, summed from k = 0 to n. Each coefficient nCk is exactly the same combination value from Permutations & Combinations — which is also why these coefficients form Pascal’s Triangle when you stack them row by row.
Worked Example
For n = 3: (x+y)³ = 1x³ + 3x²y + 3xy² + 1y³, using coefficients 3C0=1, 3C1=3, 3C2=3, 3C3=1.
Frequently Asked Questions
Q: Why are the coefficients symmetric?
Because nCk = nC(n−k) — choosing k items to leave out is the same count as choosing (n−k) items to keep. This symmetry is why Pascal’s Triangle looks the same read left-to-right or right-to-left.
Q: What’s the general term used for in exam questions?
The general term T(k+1) = nCk · x(n−k) · yk lets you find one specific term (like "the 5th term") without expanding the whole expression — a common PUC question type.
This is exactly the general-term technique covered in 1st PUC Binomial Theorem. See how Daniel Classes teaches 1st and 2nd PUC Mathematics →