### Home > A2C > Chapter 13 > Lesson 13.1.2 > Problem 13-36

13-36.

Josephina thinks that she has discovered a new pattern, shown below. Homework Help ✎

Check her equations by multiplying. Does her pattern work?

Based on her pattern, what does

equal? Is it true? **Justify**your answer.Make a conjecture about how to represent the result for

. You will probably need “, …,” in the middle of your expression.

*x* − 1 = 1(*x* − 1)

*x*^{2} − 1 = (*x* + 1) (*x* − 1)

...

Check by multiplying, as in part (a).