Factorisation of the expression $m^{4} - 1296$ , results in

(m - 9) (m + 9) (m^{2} - 18)

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(m - 6) (m + 6) (m^{2} + 36)

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(m^{2} - 6) (m^{2} + 6)

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(m^{2} - 12) (m^{2} + 12)

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Solution

The correct option is B $(m - 6) (m + 6) (m^{2} + 36)$
$m^{4} - 1296 = {(m^{2})}^{2} - {(36)}^{2}$

$= (m^{2} - 36) (m^{2} + 36)$ .... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

$= [{(m)}^{2} - {(6)}^{2}] [m^{2} + 36]$

$= (m - 6) (m + 6) (m^{2} - 36)$

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