Advanced MathMediumNumeric product that telescopes to a difference of fourth powers
Advanced Math practice question
What is the value of (3 + 1)(3 − 1)(3² + 1²)?
Answer: 80
(3 + 1)(3 − 1) = 3² − 1 = 8, and 8(3² + 1) = 8 × 10 = 80. (In general (x + y)(x − y)(x² + y²) = x⁴ − y⁴ = 81 − 1.)
Common wrong answers
- If you answered 40
- 40 is 4 × 10, dropping the factor (3 − 1) = 2.
- If you answered 64
- 64 is 4 × 2 × 8, taking 3² + 1² as 8.
- If you answered 82
- 82 adds 1 instead of subtracting: 3⁴ + 1.
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