[tex]x^3+8y^6\\\\=x^3+2^3y^{2\cdot3}\\\\=x^3+2^3(y^2)^3\qquad|\text{used}\ (a^n)^m=a^{nm}\\\\=x^3+(2y^2)^3\qquad|\text{used}\ (ab)^n=a^nb^n\\\\=(x+2y^2)(x^2-x\cdot2y^2+(2y^2)^2)\qquad|\text{used}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(x+2y^2)(x^2-2xy^2+2^2(y^2)^2)\\\\=(x+2y^2)(x^2-2xy^2+4y^4)[/tex]
