Factor COMPLETELY over the complex numbers, if possible: a4 - b4

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16-05-2018
Mathematics

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Factor COMPLETELY over the complex numbers, if possible: a4 - b4

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LammettHash LammettHash · Answer 1 · 2018-05-16T18:50:11+02:00

LammettHash LammettHash

16-05-2018

[tex]a^4-b^4=(a^2)^2-(b^2)^2=(a^2-b^2)(a^2+b^2)[/tex]

[tex]a^2-b^2=(a-b)(a+b)[/tex]

[tex]a^2+b^2=a^2-(ib)^2=(a-ib)(a+ib)[/tex]

[tex]a^4-b^4=(a-b)(a+b)(a-ib)(a+ib)[/tex]

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