Practice Binomial Theorem in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The binomial theorem gives the expansion of (a + b)^n as a sum of terms involving binomial coefficients: (a+b)^n = sum of C(n,k) * a^(n-k) * b^k. Each coefficient \binom{n}{k} counts the number of ways to choose k copies of b from n factors.
Each term of (a+b)^n picks 'a' or 'b' from each factor. \binom{n}{k} counts how many ways to pick k b's.
Example 1
mediumExpand (x + 2)^3 using the Binomial Theorem.
Example 2
hardFind the coefficient of x^3 in the expansion of (2x + 3)^5.
Example 3
easyExpand (a + b)^4 using Pascal's triangle.
Example 4
mediumWhat is \binom{6}{2}?