Pascal's Triangle

In class this week, we learned about Pascal's Triangle. This is a very useful method of expanding binomials, as I will demonstrate with a quick example.
Imagine that you have the following binomial:

(a + b)^5

To find the coefficients for this expansion, you would have to consult Row 5 of Pascal's triangle:

The coefficients for Row 5 are:

1  5  10  10  5  1

Now, you must place these coefficients before each term. The first term (a) will decrease in power from left to right, while the second term (b) will increase in power from left to right.

(1*a^5*b^0) + (5*a^4*b^1) + (10*a^3*b^2) + (10*a^2*b^3) + (5*a^1*b^4) + (1*a^0*b^5)

When simplified, this is equal to:

a^5 + 5(a^4)(b) + 10(a^3)(b^2) + 10(a^2)(b^3) + 5(a)(b^4) + b^5

Finally, we have expanded this binomial using Pascal's triangle. Expanding the binomial by using the F.O.I.L. method would have also worked, although it would have taken significantly longer and required a much greater amount of work also.