a⁹-a, factorise this
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Answer:
a^9-a
=a(a^8-1)
=a{(a^4)^2-1^2}
=a(a^4+1)(a^4-1)
=a(a^4+1){(a^2)^2-1^2}
=a(a^4+1)(a^2+1)(a^2-1)
=a(a^4+1)(a^2+1)(a+1)(a-1)
Verified answer
[tex] \sf \red{a⁹-a}[/tex]
[tex] \sf \blue{GCF = a}[/tex]
[tex] \sf \pink{a(\frac{{a}^{9}}{a}-\frac{a}{a})}[/tex]
[tex] \sf\purple{a({a}^{8}-1)}[/tex]
[tex] \sf \green{a({({a}^{4})}^{2}-{1}^{2})}[/tex]
[tex] \sf \color{gold} a({a}^{4}+1)({a}^{4}-1)[/tex]
[tex] \sf \orange{a({a}^{4}+1)({({a}^{2})}^{2}-{1}^{2})}[/tex]
[tex] \sf\color{violet}a({a}^{4}+1)({a}^{2}+1)({a}^{2}-1)[/tex]
[tex] \sf \color{pink}a({a}^{4}+1)({a}^{2}+1)({a}^{2}-{1}^{2})[/tex]
[tex]\sf\color{green}a({a}^{4}+1)({a}^{2}+1)(a+1)(a-1)[/tex]