Find the coefficient of the x^2 term in in the expansion of (1+x)^4.

To get an example of what this question is asking: the expansion of (1+x)^2 can be found by distributing and gives 1+2x+x^2. The coefficient of the x^2 term here would be 1, and for the x^1 term it would be two. In our case, we shouldn't expand by distributing each factor. Instead, this can be worked out with Pascal's triangle: 1 1; 1 2 1; 1 3 3 1; 1 4 6 4 1 where each entry is the sum of the two above it. In our case we have the triangle down to the 4th row as we have (1+x)^4, and since we need the x^2 term, counting from 0 to 2 across this row we get the coefficient 6. This can also be calculated without Pascal's triangle via the formula for binomial coefficients: n!/k!/(n-k)! which in our case is 4!/2!/2!=43/21=6.