1. **Stating the problem:** We need to find the odd one out among the following expressions: 1. $45^2$ 2. $9^2 \times 5^2$ 3. $117^2 - 108^2$ 4. $1014^2 - 1013^2$ 5. $27^2 + 36^2$ 2. **Recall important formulas and rules:** - The square of a product: $a^2 \times b^2 = (ab)^2$ - Difference of squares: $a^2 - b^2 = (a-b)(a+b)$ - Sum of squares: $a^2 + b^2$ (no simple factorization over the reals) 3. **Evaluate or simplify each expression:** 1. $45^2 = 2025$ 2. $9^2 \times 5^2 = (9 \times 5)^2 = 45^2 = 2025$ 3. $117^2 - 108^2 = (117 - 108)(117 + 108) = 9 \times 225 = 2025$ 4. $1014^2 - 1013^2 = (1014 - 1013)(1014 + 1013) = 1 \times 2027 = 2027$ 5. $27^2 + 36^2 = 729 + 1296 = 2025$ 4. **Analyze results:** - Expressions 1, 2, 3, and 5 all equal 2025. - Expression 4 equals 2027, which is different. 5. **Conclusion:** The odd one out is expression 4: $1014^2 - 1013^2$ because it does not equal 2025 like the others. **Final answer:** Expression 4 is the odd one out.