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JAMB 2012 · UTME · Q8✱✱

Simplify (6+2)2−(6−2)2(\sqrt6 + 2)^2 - (\sqrt6 - 2)^2.

Worked solution (try it first)
  1. Expand the first square: (6+2)2=6+46+4(\sqrt6 + 2)^2 = 6 + 4\sqrt6 + 4, which is 10+4610 + 4\sqrt6.
  2. Expand the second: (6−2)2=6−46+4(\sqrt6 - 2)^2 = 6 - 4\sqrt6 + 4, which is 10−4610 - 4\sqrt6.
  3. Subtract: (10+46)−(10−46)=86(10 + 4\sqrt6) - (10 - 4\sqrt6) = 8\sqrt6, option C.

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