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64a^{6}-48b^{2}a^{4}+12b^{4}a^{2}-b^{6}
Consider 64a^{6}-48a^{4}b^{2}+12a^{2}b^{4}-b^{6} as a polynomial over variable a.
\left(4a^{2}-b^{2}\right)\left(16a^{4}-8a^{2}b^{2}+b^{4}\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 64a^{6} and n divides the constant factor -b^{6}. One such factor is 4a^{2}-b^{2}. Factor the polynomial by dividing it by this factor.
\left(2a-b\right)\left(2a+b\right)
Consider 4a^{2}-b^{2}. Rewrite 4a^{2}-b^{2} as \left(2a\right)^{2}-b^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
16a^{4}-8b^{2}a^{2}+b^{4}
Consider 16a^{4}-8a^{2}b^{2}+b^{4}. Consider 16a^{4}-8a^{2}b^{2}+b^{4} as a polynomial over variable a.
\left(4a^{2}-b^{2}\right)\left(4a^{2}-b^{2}\right)
Find one factor of the form ua^{v}+w, where ua^{v} divides the monomial with the highest power 16a^{4} and w divides the constant factor b^{4}. One such factor is 4a^{2}-b^{2}. Factor the polynomial by dividing it by this factor.
\left(2a-b\right)\left(2a+b\right)
Consider 4a^{2}-b^{2}. Rewrite 4a^{2}-b^{2} as \left(2a\right)^{2}-b^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
\left(2a-b\right)^{3}\left(2a+b\right)^{3}
Rewrite the complete factored expression.