Find the product of $(x - 2) (x + 2) (x^{2} + 4) (x^{4} + 16)$

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Solution

use the identity $(a - b) (a + b) = (a^{2} - b^{2})$
we have
$(x - 2) (x + 2) = x^{2} - 4$
$(x^{2} - 4) (x^{2} + 4) = (x^{4} - 16)$
$(x^{4} - 16) (x^{4} + 16) = (x^{8} - 256)$
hence $(x - 2) (x + 2) (x^{2} + 4) (x^{4} + 16) = (x^{8} - 256)$

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