1. Stating the problem: Simplify the expression $3(m+n)^2$. 2. Recall the formula for the square of a binomial: $$(a+b)^2 = a^2 + 2ab + b^2$$ 3. Apply the formula to $(m+n)^2$: $$(m+n)^2 = m^2 + 2mn + n^2$$ 4. Multiply the entire expression by 3: $$3(m+n)^2 = 3(m^2 + 2mn + n^2)$$ 5. Distribute the 3: $$3m^2 + 6mn + 3n^2$$ 6. Final simplified expression is $$3m^2 + 6mn + 3n^2$$