The Binomial TheoremThe expansion of a binomial power, and where Pascal's triangle comes from.MathematicsThe expansion of (x + y)ⁿ sums C(n, k) x^(n−k) y^kover k from 0 to n.(x + y)ⁿ = Σ C(n, k) x^(n−k) y^k(x + y)³x³ + 3x²y + 3xy² + y³Row 3 of Pascal.x²y³ in (x + y)⁵C(5, 2) = 10Choose where the x go.Σ C(n, k) over all k2ⁿSet x = y = 1.THE COMMON MISTAKE✗ (x + y)ⁿ = xⁿ + yⁿ✓ Every cross term appears as wellOnly n = 1 makes that true. Squaring gives x² + 2xy + y²; the middle term countsthe two ways of picking one x and one y.Pascal's triangle: C(n, k) = C(n − 1, k − 1) + C(n − 1, k). Each entry is thesum of the two directly above it.The Binomial Theoremlearnposters.com
The Binomial Theorem — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the The Binomial Theorem poster

The rule, 3 worked examples, and the mistake everyone makes.

Pascal's triangle: C(n, k) = C(n − 1, k − 1) + C(n − 1, k). Each entry is the sum of the two directly above it.

Questions about the The Binomial Theorem poster

What’s on the The Binomial Theorem poster?
The rule, 3 worked examples, and the mistake everyone makes. The expansion of (x + y)ⁿ sums C(n, k) x^(n−k) y^k over k from 0 to n.; (x + y)ⁿ = Σ C(n, k) x^(n−k) y^k; (x + y)³ = x³ + 3x²y + 3xy² + y³; x²y³ in (x + y)⁵ = C(5, 2) = 10; Σ C(n, k) over all k = 2ⁿ; Common mistake: (x + y)ⁿ = xⁿ + yⁿ → Every cross term appears as well. Pascal's triangle: C(n, k) = C(n − 1, k − 1) + C(n − 1, k). Each entry is the sum of the two directly above it.
Who is the The Binomial Theorem poster for?
The Binomial Theorem belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning discrete mathematics can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the The Binomial Theorem poster?
For a single coefficient without expanding, and for counting-identity proofs. A wall chart earns its place by being glanceable from where the work is happening, so The Binomial Theorem belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with The Binomial Theorem?
Counting Principles, Euler & Hamiltonian Paths and Graph Vocabulary sit alongside The Binomial Theorem in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Counting PrinciplesEuler & Hamiltonian PathsGraph Vocabulary
Is the The Binomial Theorem poster free to download and print?
Yes. The Binomial Theorem downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the The Binomial Theorem poster print at?
The Binomial Theorem is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of The Binomial Theorem loses nothing.Printing guide

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