Advanced MathMediumExpanding a difference of cubes
Advanced Math practice question
Which expression is equivalent to (x − 2)(x² + 2x + 4)?
- A. x³ − 8Correct
- B. x³ + 8
- C. x³ − 4x − 8
- D. x³ − 2x² − 8
Answer: A. x³ − 8
Distribute: x(x² + 2x + 4) − 2(x² + 2x + 4) = x³ + 2x² + 4x − 2x² − 4x − 8. The middle terms cancel, leaving x³ − 8.
Why the other answers are wrong
- B. x³ + 8
- The constant is −2 × 4 = −8, not +8.
- C. x³ − 4x − 8
- The 4x from x · 4 and the −4x from −2 · 2x cancel; there is no x term left.
- D. x³ − 2x² − 8
- The 2x² from x · 2x and the −2x² from −2 · x² cancel; there is no x² term left.
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