$${ a }^{ 6 } + { a }^{ 2 } { b }^{ 2 } - { a }^{ 4 } -a { b }^{ 2 }$$
Factor
$a\left(a-1\right)\left(a^{4}+a^{3}+b^{2}\right)$
Solution Steps
Factor out $a$.
$$a\left(a^{5}+ab^{2}-a^{3}-b^{2}\right)$$
Consider $a^{5}+ab^{2}-a^{3}-b^{2}$. Consider $a^{5}+ab^{2}-a^{3}-b^{2}$ as a polynomial over variable $a$.
$$a^{5}-a^{3}+b^{2}a-b^{2}$$
Find one factor of the form $a^{k}+m$, where $a^{k}$ divides the monomial with the highest power $a^{5}$ and $m$ divides the constant factor $-b^{2}$. One such factor is $a-1$. Factor the polynomial by dividing it by this factor.
