### Home > INT3 > Chapter 10 > Lesson 10.2.2 > Problem 10-125

10-125.

**10-125.**Josephina thinks that she has discovered a new pattern, shown at right. 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 need “…” in the middle of your expression.

To check a division problem using multiplication, multiply the divisor by the quotient. In the second case, multiply (*x* − 1)(*x* + 1). Does it equal *x*^{2} − 1? How will you check the third and fourth cases?

Look for a pattern in the quotients. Look at the number of terms and the exponent on each term.