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Factorization — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSFactorization1 Mark
MCQ
The factors of $m^2 - 256$ are:
  • A
    $(m + 4)^2$
  • B
    $(m - 4)^2$
  • C
    $(m - 4) (m + 4)$
  • ✓
    None of the above.
✓

Answer

Correct option: D.
None of the above.
$m^4 = (m^2)^2\ \  and\ \  256 = (16)^2$
$m^4 - 256 = (m^2)^2 - (16)^2 = (m^2 - 16) (m^2 + 16)$
$m^2 - 16 = m^2 - 4^2 = (m - 4) (m + 4)$
$m^4 - 256 = (m - 4) (m + 4) (m^2 + 16)$

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