Learning Resources

Lesson

In this lesson we will explore the relationship of Pascal's Triangle to the expansion of the expression (x + 1)ⁿ.  To see this relationship we need to write the expansion of (x + 1)ⁿ for values of n from at least 0 to 4. This is done in a step by step approach below so you can see how the power was expanded.

You should complete at least the expansion for the power of 5 as required in Investigation 14 on page 342. Note that the power of the binomial corresponds to the row number of Pascal's Triangle. Thus row n of Pascal's Triangle should give the coefficients of (x + 1)ⁿ .

Activity

1. Complete Investigation 14 on page 342 of your text. If you have worked through the lesson, you will have much of Step A already completed . 
2. Complete the Investigation Questions 9 & 10 on page 343. You should work through 10 using the same approach as used in the lesson.
3. Do the CYU Questions 11 - 14 on page 343.

When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.

Test Yourself

• Use your knowledge of Pascal's Triangle to write the first four terms of (x + 1)¹⁵ .

Solution