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Mathematics

Simplify (x - 2)(x + 2)(x² + 4)(x⁴ + 16).

Expansions

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Answer

As (a - b)(a + b) = (a² - b²)

On solving,

$(x - 2)(x + 2)(x^2 + 4)(x^2 + 16) = (x^2 - 4)(x^2 + 4)(x^4 + 16) \\[1em] = (x^4 - 16)(x^4 + 16) \\[1em] = ((x^4)^2 - 16^2) \\[1em] = x^8 - 256.$

On simplifying we get, (x - 2)(x + 2)(x² + 4)(x⁴ + 16) = x⁸ - 256.

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