State True or False.
$p^{4} - 81 q^{4}$ $= (p + 3 q) (p - 3 q) (p^{2} + 9 q^{2})$

True

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False

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Solution

The correct option is A True
$p^{4} - 81 q^{4} = [(p^{2})^{2} - (9 q^{2})^{2}]$
$= (p^{2} + 9 q^{2}) (p^{2} - 9 q^{2})$
$= (p^{2} + 9 q^{2}) [(p)^{2} - (3 q)^{2})]$
$= (p^{2} + 9 q^{2}) [(p - 3 q) (p + 3 q)]$
$= (p^{2} + 9 q^{2}) (p - 3 q) (p + 3 q)$

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