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The expanded form of the given expression \((y+1)^2 + 2(y+1) + 1\) is:

\[
y^2 + 4y + 4
\]

Would you like more details on how this expansion was done, or do you have any specific questions?

Here are some related questions to consider:
1. How do you expand any binomial expression like \((x+a)^2\)?
2. What are the steps to combine like terms in algebraic expressions?
3. How do you factor a quadratic expression like \(y^2 + 4y + 4\)?
4. What is the geometric interpretation of squaring binomials?
5. How would the expression change if it had a negative sign before the binomials?

**Tip:** When expanding binomials, always apply the distributive property (also known as FOIL for two binomials).

Learn how to expand the expression (y+1)^2 + 2(y+1) + 1 into its simplest form, yielding y^2 + 4y + 4. This problem covers key concepts in algebra including binomial expansion and simplifying quadratic expressions. Suitable for students in Grades 8-10.

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