Gujarat BoardEnglish MediumSTD 8MATHSFactorization1 Mark
MCQ
The factors of $\mathrm{m}^{2}-256$ 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
d $\mathrm{m}^{4}=\left(\mathrm{m}^{2}\right)^{2}$ and $256=(16)^{2}$
$\mathrm{m}^{4}-256=\left(\mathrm{m}^{2}\right)^{2}-(16)^{2}=\left(\mathrm{m}^{2}-16\right)\left(\mathrm{m}^{2}+16\right)$
$\mathrm{m}^{2}-16=\mathrm{m}^{2}-4^{2}=(\mathrm{m}-4)(\mathrm{m}+4)$
$\mathrm{m}^{4}-256=(\mathrm{m}-4)(\mathrm{m}+4)\left(\mathrm{m}^{2}+16\right)$
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