1. **State the problem:** Fully factorise the expression $15p^2 + 24p$. 2. **Identify the greatest common factor (GCF):** The coefficients 15 and 24 have a GCF of 3, and both terms contain the variable $p$ with the lowest power being $p^1$. 3. **Extract the GCF:** $$15p^2 + 24p = 3p(\cancel{5p} + \cancel{8})$$ 4. **Simplify inside the parentheses:** $$3p(5p + 8)$$ 5. **Final answer:** The fully factorised form is $3p(5p + 8)$. This means we took out the common factor $3p$ from both terms, leaving the simplified expression inside the parentheses.