Binomial Theorem Part 6

Mar
20

Filed Under CSET Math |

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This is part 6 in our series on the binomial theorem for teacher candidates studying for the CSET Math examination.

There is an easier way to expand an expression: Pascale’s Triangle.

In mathematics, Pascal’s triangle is a geometric arrangement of the binomial coefficients in a triangle. It is named after Blaise Pascal in much of the western world, although other mathematicians studied it before him in India, Persia, China, and Italy.

Here it is below:

                             1
                           1   1
                         1   2   1
                       1   3   3   1
                     1   4   6   4   1
                   1   5  10   10  5   1
                 1   6  15  20   15  6   1
               1   7  21  35   35  21  7   1
                             .
                             .
                             .

You start out with the top two rows: 1, and 1, 1. Then to construct each entry in the next row, you look at the two entries above it (i.e. the one above it and to the right, and the one above it and to the left). At the beginning and the end of each row, when there’s only one number above, put a 1. You add up the number above and to the left and the number above and to the right.

Example:

Approximate (1.02)5 without a calculator. Show your work in the space below.

First, use Pascal’s Triangle to expand (1 + 2x)5

We have a power of 5 so we use the 5th row in Pascal’s Triangle which is: 1, 5, 10, 10, 5, 1

cset math

Did you hear about the teacher who was arrested trying to board an airplane with a compass, a protractor and a calculator?

He was charged with carrying weapons of math instruction.

By Maureen Miranda
http://www.ACEtheCSET.com
Maureen Miranda

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