Square the middle term of three consecutive numbers and subtract the product of the remaining two. Repeat this process for other number sets. Identify the pattern formed and represent it algebraically. Expand both sides to verify the 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 \(p\).]
The obtained algebraic identity is .