1. The problem is to evaluate the expression $5(9^2 - 7^2) - 35$ and determine which given statements about it are correct. 2. Recall the order of operations: first evaluate exponents, then parentheses, then multiplication, and finally subtraction. 3. Calculate the squares inside the parentheses: $$9^2 = 81$$ $$7^2 = 49$$ 4. Substitute these values back into the expression inside the parentheses: $$9^2 - 7^2 = 81 - 49 = 32$$ 5. Multiply by 5: $$5(32) = 160$$ 6. Now subtract 35: $$160 - 35 = 125$$ 7. Check each statement: - A: $5(9^2 - 7^2) = 20$ is incorrect because $5(32) = 160$, not 20. - B: $5(9^2 - 7^2) = 5(32)$ is correct as shown in step 4. - C: $5(9^2 - 7^2) = 160$ is correct as shown in step 5. - D: $5(9^2 - 7^2) - 35 = -15$ is incorrect because the result is 125, not -15. - E: $5(9^2 - 7^2) - 35 = 125$ is correct as shown in step 6. Final answer: Statements B, C, and E are correct.