16Hit1600
Advanced MathMediumExpanding a scaled squared binomial

Advanced Math practice question

Which expression is equivalent to 2(x − 3)² + 5?

  1. A. 2x² − 12x + 23Correct
  2. B. 2x² − 6x + 14
  3. C. 2x² + 23
  4. D. 2x² − 12x + 14

Answer: A. 2x² − 12x + 23

(x − 3)² = x² − 6x + 9, so 2(x − 3)² + 5 = 2x² − 12x + 18 + 5.

Why the other answers are wrong

B. 2x² − 6x + 14
This doubles only the x² term.
C. 2x² + 23
This drops the middle term.
D. 2x² − 12x + 14
This forgets to double the 9 before adding 5.

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