Answer
$x(1+2x)(1-2x+4x^2)$
Work Step by Step
The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$.
The formula for factoring the difference of two cubes is: $A^3-B^3=(A-B)(A^2+AB+B^2)$.
Hence here: $x+8x^4=\\=x(1+8x^3)\\=x(1+(2x)^3)\\=x(1+2x)(1^2-2x+(2x)^2)\\=x(1+2x)(1-2x+4x^2)$
