Binomial expansion

Expansion of common powers

• …

Pascal’s triangle

The coefficients in the expansions above correspond to the rows of Pascal’s triangle:

row |
  0 |              1
  1 |            1   1
  2 |          1   2   1
  3 |        1   3   3   1
  4 |      1   4   6   4   1
  5 |    1   5  10  10   5   1
  6 |  1   6  15  20  15   6   1
       ^                   ^
       |_ column 0         |_ column 5

We can write the the coefficient at row and column as .

Finding specific terms using a calculator

If we want to find the coefficient of the term of the expansion of , we can solve:

Finding a specific term using factorials

If we want to find , we can also use this formula:

Finding all the coefficients

Expand

Expand

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• Answer:

Representing the number of combinations

We can write the number of combinations of choosing items from a list of items as either or .

Common combinations