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Algebra Level 3

( x + m − 1 2 ) 2 + ( x + m + 1 2 ) 2 + 2 ( x 2 − 2 m x + m 2 − 1 4 ) 2 \left(x + m - \dfrac{1}{2}\right)^2 + \left(x + m + \dfrac{1}{2}\right)^2 + 2\left(x^2 - 2mx + m^2- \dfrac{1}{4}\right)^2

Can the expression above be factorized for all real x x and m m ?

Bonus

  • If the expression can be factorized, factorize it.
  • If not, find that values of m m for which the expression can be factorized?
The expression is unfactorizable. The expression is factorizable.

Thành Đạt Lê by Thành Đạt Lê , 17, Singapore

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