Which of the following expressions is equivalent to 2(x − 4)2 − 5x?

Explanation

To simplify 2(x − 4)2 − 5x, start by expanding the squared term: (x − 4)2 = x2 − 8x + 16. Then distribute the 2 across these terms: 2(x2 − 8x + 16) = 2x2 − 16x + 32. Next, subtract 5x, resulting in 2x2 − 16x + 32 − 5x. Combine the like terms −16x and −5x to get 2x2 − 21x + 32. This matches option A, which is the correct answer. Option B incorrectly simplifies the constant term as negative. Option C has an incorrect x coefficient, and option D has errors in both the x coefficient and constant term.