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 x2 − 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.