Let's simplify the expression $5 + 2(m - 2)^2$.

1. Expand the squared term:

$(m - 2)^2 = m^2 - 4m + 4$

2. Substitute this back into the original expression:

$5 + 2(m^2 - 4m + 4)$

3. Distribute the $2$ across the terms inside the parentheses:

$5 + 2m^2 - 8m + 8$

4. Combine like terms (constant terms $5 + 8$):

$2m^2 - 8m + 13$

So, the simplified expression is:

$2m^2 - 8m + 13$

Would you like further clarification or details? Let me know if you'd like to see any specific steps!

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Here are 5 related questions to explore further:

1. How do you expand binomials like $(m - 2)^2$ using the formula $(a - b)^2$?
2. What are the steps to solve quadratic equations like $2m^2 - 8m + 13 = 0$?
3. How does distributing terms work in algebra, and why is it necessary?
4. How can you factor a quadratic expression like $2m^2 - 8m + 13$?
5. What happens if the expression had a different power, such as $(m - 2)^3$?

Tip: When simplifying expressions with exponents, always make sure to expand or simplify terms fully before combining like terms.