Why is x^4 - 16 when factored not just (x^2 + 4) (x^2 - 4)?

asked Jan 11, 2021 115k views

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Answer:

$(x - 2)(x + 2)( {x}^(2) + 4)$

Explanation:

${x}^(4) - 16 \\ = ({x}^(2))^(2) - ({2}^(2))^(2) \\ = ( {x}^(2) - {2}^(2) )( {x}^(2) + {2}^(2) ) \\ = (x - 2)(x + 2)( {x}^(2) + 4)$

Because
(x^2 - 4) = (x^2-2^2) can further be factorised as (x - 2) (x + 2).

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