Choose three progressive numbers, square the middle one, and subtract the product of the other two. Repeat the same with other sets of numbers. What pattern do you notice? How do we write this as an algebraic equation? Expand both sides of the equation to check that it is a true identity.
Answer:
For any three consecutive numbers, square the middle one, and subtracting the product of the other two numbers gives the answer .
The pattern observed is .
[Note: Enter the answer in terms of the varible \(y\).]
The obtained algebraic identity is .