Find the product of $(p + 2) (p - 2) (p^{2} + 4)$

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Solution

We know that $(a - b) (a + b) = a^{2} - b^{2}$
So $(p + 2) (p - 2) = p^{2} - (2)^{2}$
$(p + 2) (p - 2) = p^{2} - 4$
So $(p^{2} - 4) (p^{2} + 4)$
$= (p^{2})^{2} - (4)^{2}$
$= p^{4} - 16$

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