Which of the following expressions is equivalent to 2(x − 4)2 − 5x?
Correct answer: A. 2x2−21x+32
- A. 2x2−21x+32
- B. 2x2−21x−32
- C. 2x2−13x+32
- D. 2x2−16x−21
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.
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