factorize 25a⁶-25b⁶, we get
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Try replacing x with u2 to clear the fractional exponents.
If u2=x, we get 3x3/2−9x1/2+6x−1/2=3(u2)3/2−9(u2)1/2+6(u2)−1/2 =3u3−9u+6u−1
Next, factor out u−1 and get 3u−1(u4−3u2+2).
This is now quadratic in u2 (which is x) so we get 3x−1/2(x2−3x+2)=
3(x−2)(x−1)x−−√
Of course, you can avoid introducing u if you see that factoring out x−1/2 at the beginning leaves you with a quadratic in x.
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