Разложите на множители ay^7+y^7-ay^3-y^3.

\[ay^{7} + y^{7} - ay^{3} - y^{3} =\]

\[= y^{7}(a + 1) - y^{3}(a + 1) =\]

\[= (a + 1)\left( y^{7} - y^{3} \right) = y^{3}(a + 1)\left( y^{4} - 1 \right) =\]

\[= y^{3}(a + 1)\left( y^{2} - 1 \right)\left( y^{2} + 1 \right) =\]

\[= y^{3}(a + 1)(y - 1)(y + 1)\left( y^{2} + 1 \right)\]