Question

Factor a^9-b^9

Answer 1

\(\bf a^9-b^9\implies (a^3)^3-(b^3)^3\\\qquad \\
recall\implies a^3-b^3 = (a-b)(a^2+ab+b^2)\)

Answer 2

\[But you can factor (a^3+a^3b^3+b^6), this is where I get stuck\]

Answer 3

\(\bf a^9-b^9\implies (a^3)^3-(b^3)^3
\\ \quad \\
recall\implies {\color{blue}{ a^3-b^3 = (a-b)(a^2+ab+b^2)}}
\\ \quad \\

(a^3)^3-(b^3)^3\implies {\color{blue}{ (a^3-b^3)}}[(a^3)^2+a^3b^3+(b^3)^2]
\\ \quad \\
\implies {\color{blue}{ (a-b)(a^2+ab+b^2)}}[(a^3)^2+a^3b^3+(b^3)^2]
\\ \quad \\
\implies (a-b)(a^2+ab+b^2)(a^6+a^3b^3+b^6)\)

Answer 4

(a-b)*(a^2+a*b+b^2)*(a^6+a^3*b^3+b^6)