The problem asks to expand and simplify $(b + 3)^2$.

Step-by-step solution:

1. Use the binomial expansion formula: $(x + y)^2 = x^2 + 2xy + y^2$

2. Substitute $x = b$ and $y = 3$: $(b + 3)^2 = b^2 + 2(b)(3) + 3^2$

3. Simplify each term:

   • $b^2$ remains $b^2$,
   • $2(b)(3) = 6b$,
   • $3^2 = 9$.

4. Combine all terms: $b^2 + 6b + 9$

Final Answer:

$(b + 3)^2 = b^2 + 6b + 9$

Would you like further clarification or additional examples?

Related Questions:

1. How would you expand and simplify $(b - 3)^2$?
2. What is the general formula for expanding $(x + y)^n$ when $n = 2$?
3. Can you rewrite $(b + 3)^2$ in factored form?
4. How do you use the distributive property to verify the expansion?
5. How does this apply to problems involving area in geometry?

Tip:

When squaring binomials, remember the middle term $2xy$ often accounts for mistakes—double-check it!