Algebra › Section L · Sequences, series, and the binomial theorem › Topic L.4
The binomial theorem
Multiply (x + y)⁵ by hand and you will grind through dozens of terms before the dust settles. The binomial theorem is the shortcut: the expansion's shape is completely predictable, its coefficients hide in a triangle, and one formula finds any single term without expanding anything at all.
In this topic
- Why the theorem exists
- The shape of an expansion
- Pascal's triangle: the coefficient machine
- Worked example: an expansion with alternating signs
- Factorials: the counting shorthand
- Binomial coefficients: n choose r
- Worked example: the theorem in action
- One term, no expansion
- Common mistakes to avoid
- Key takeaways
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