Question

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

Answer 1

Answer:

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

Step-by-step 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).