How do you factor 108m3−500?

1 Answer
MattyMatty
Mar 18, 2018

=(3m−5)(6m+5(1+√3i))(6m+5(1−√3i))

Explanation:

108=4⋅27=4⋅33
500=4⋅125=4⋅53
So we have
4((3m)3−53)
Now we apply a3−b3=(a−b)(a2+ab+b2)
=4(3m−5)(9m2+15m+25)
The quadratic factor can also be factored in factors
with complex numbers as follows :
disc : 152−4⋅9⋅25=−675=−27⋅25=−27⋅52
⇒m=−15±5√27i18
⇒m=−5±5√3i6
⇒m=−(56)(1±√3i)
⇒9(m+(56)(1+√3i))(m+(56)(1−√3i))
So we get
36(3m−5)(m+(56)(1+√3i))(m+(56)(1−√3i))
=(3m−5)(6m+5(1+√3i))(6m+5(1−√3i))

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