1. Problem statement: We want to understand how the term $3ab$ appears in the expansion of $(a+b)^3$. 2. Recall the binomial expansion formula for cubes: $$(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$$ 3. Group the middle terms: $$3a^2b + 3ab^2 = 3ab(a + b)$$ 4. So the full expansion can be written as: $$(a+b)^3 = a^3 + b^3 + 3ab(a+b)$$ 5. This shows that the $3ab$ term comes from combining the coefficients of $a^2b$ and $ab^2$ terms, factoring out $3ab$. 6. Therefore, the identity used is: $$a^3 + b^3 = (a+b)^3 - 3ab(a+b)$$ This explains how the $3ab$ term arises in the formula.