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I know how to get from here:
-2(w-5)(w+5)(w^2+25)
to here:
-2w^4+1250
But I don't know how to get from here:
-2w^4+1250
to here:
-2(w-5)(w+5)(w^2+25)
The same with this problem:
a^9-1
(a-1)(a^2+a+1)(a^6+a^3+1)
Its always difficult to find the factors, given the simplest form.
a^3 - b^3 is (a-b)(a^2 + ab + b^2).
If one of the factors is known, it becomes a bit easier.
For lower degrees, by remembering some formulae, it can be done easily.
Like a^2 - b^2 = (a+b) x (a-b),
(a^3 + b^3) = (a+b) x (a^2 - ab + b^2) etc.
When you are aksed to prove that the LHS is equal to the RHS,
it is always better to start with lower degrees.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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