Question

a⁹-a, factorise this​

Answer 1

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)

Answer 2

$\sf \red{a⁹-a}$

$\sf \blue{GCF = a}$

$\sf \pink{a(\frac{{a}^{9}}{a}-\frac{a}{a})}$

$\sf\purple{a({a}^{8}-1)}$

$\sf \green{a({({a}^{4})}^{2}-{1}^{2})}$

$\sf \color{gold} a({a}^{4}+1)({a}^{4}-1)$

$\sf \orange{a({a}^{4}+1)({({a}^{2})}^{2}-{1}^{2})}$

$\sf\color{violet}a({a}^{4}+1)({a}^{2}+1)({a}^{2}-1)$

$\sf \color{pink}a({a}^{4}+1)({a}^{2}+1)({a}^{2}-{1}^{2})$

$\sf\color{green}a({a}^{4}+1)({a}^{2}+1)(a+1)(a-1)$