1. **State the problem:** Simplify the expression $80p^{2} - 45s^{2}$ by factoring. 2. **Identify the formula:** This is a difference of squares problem if it can be expressed as $a^{2} - b^{2} = (a - b)(a + b)$, or it can be factored by taking out the greatest common factor (GCF). 3. **Find the GCF:** The coefficients 80 and 45 have a GCF of 5. 4. **Factor out the GCF:** $$80p^{2} - 45s^{2} = 5(\cancel{16} \times p^{2} - \cancel{9} \times s^{2})$$ 5. **Recognize the difference of squares inside the parentheses:** $$16p^{2} - 9s^{2} = (4p)^{2} - (3s)^{2}$$ 6. **Apply the difference of squares formula:** $$a^{2} - b^{2} = (a - b)(a + b)$$ So, $$16p^{2} - 9s^{2} = (4p - 3s)(4p + 3s)$$ 7. **Write the fully factored form:** $$80p^{2} - 45s^{2} = 5(4p - 3s)(4p + 3s)$$ **Final answer:** $$5(4p - 3s)(4p + 3s)$$