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Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials1 Mark
MCQ
x3 + y3 + z3 - 3xyz is:
  • A
    (x + y + z)3
  • B
    (x - y + z)3
  • C
    (x + y + z)3 - 3xyz
  • D
    (x + y + z) (x2 + y2 + z2 - xy - yz - zx)
✓

Answer

  1. (x + y + z) (x2 + y2 + z2 - xy - yz - zx)
    Solution:
    x3 + y3 + z3 - 3xyz = x3 + y3 + 3x2y + 3xy2 + z3 - 3xyz - 3x2y - 3xy2
    = (x + y)3 +z3 - 3xy(x + y + z)
    = (x + y + z) ((x + y)2 + z2 - (x + y)z) - 3xy(x + y + z)
    = (x + y + z) (x2 + 2x2y + y2 + z2 - xy - xz - 3xy)
    = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)

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