Factorize

$m^{4} - 256$ [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

$m^{4} - 256 = (m^{2})^{2} - 16^{2}$

$(m^{2} - 16) (m^{2} + 16)$

Now, $(m^{2} + 16)$ cannot be factorised further, but $(m^{2} - 16)$ is factorisable again.

$m^{2} - 16 = m^{2} - 4^{2}$

$= (m - 4) (m + 4)$

Therefore, $m^{4} - 256 = (m - 4) (m + 4) (m^{2} + 16)$

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