Question

factorise p^8 -1/p^8

Answer 1

p^8 - 1/p^8

(p^4)^2 - (1/p^4)^2
(p^4 + 1/p^4) (p^4 - 1/p^4)
(p^4 + 1/p^4) ((p^2)^2 - (1/p^2)^2)
(p^4 + 1/p^4) (p^2 + 1/p^2)(p^2 - 1/p^2)
(p^4 + 1/p^4) (p^2 + 1/p^2)((p^√2)^2 - p^√2)^2)
(p^4 + 1/p^4) (p^2 + 1/p^2)(p+√2)(p-√2)

Answer 2

here is your answer

${p}^{8} - ( \frac{1}{p} {)}^{8} \\ \\ { ({p}^{4}) }^{2} - ( \frac{1}{p {}}^{4} {)}^{2} \\ \\( {p}^{4} - { \frac{1}{p} }^{4} )( {p}^{4} + \frac{1}{p {}}^{4} ) \\ \\( {p}^{2} - { \frac{1}{p} }^{2} )( {p}^{2} + { \frac{1}{p} }^{2} )( {p}^{4} + { \frac{1}{p} }^{4} ) \\ \\ (p + \frac{1}{p} )(p - \frac{1}{p} )( {p}^{2} + { \frac{1}{p} }^{2} )( {p}^{4} + { \frac{1}{p} }^{4} )$
hope his helps you
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