Question

ay^7 + y^7 - ay^3 - y^3​

Answer 1

$ay^7+y^7-ay^3-y^3=(a+1)y^7-y^3(a+1)=\\\\=(a+1)(y^7-y^3)=(a+1)\cdot y^3\, (y^4-1)=\\\\=y^3\cdot (a+1)(y^2-1)(y^2+1)=y^3\cdot (a+1)\cdot (y-1)\cdot (y+1)\cdot (y^2+1)$