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)
x2 − 1 = (x + 1) (x − 1)
Check by multiplying, as in part (a).