Factorize: `a^7+a b^6`

Explanation

`a+ab^6=a(a^6+b^6)`
`=a{(a^2)^3 + (6^2)^3)`
`= a(a^2+ b^2) ((a^2)^2+(b^2)^2`
` = (a^2)(b^2))`
`=a(a^2+b^2(a+ba^2b^2)`
`=a(a^2+b^2(a+b+2a2b^2-2a^2b^2-a^2b^2)`
`= a(a + b^2) ((a+b^2)^2-(sqrt3 ab)^2)a(a^2+b^2)(a+b^2-sqrt3 ab)(a^2+ b^2 + sqrt3 ab)`