Answer
$(x^2+1)\sqrt[3] {(x+1)^4}-\sqrt[3] {(x+1)^7}=(x+1)x(x-1)\sqrt[3] {x+1}$
Work Step by Step
$(x^2+1)\sqrt[3] {(x+1)^4}-\sqrt[3] {(x+1)^7}$
$(x^2+1)\sqrt[3] {(x+1)^3(x+1)}-\sqrt[3] {(x+1)^6(x+1)}$
$(x^2+1)(x+1)\sqrt[3] {x+1}-(x+1)^2\sqrt[3] {x+1}$
$(x^3+x^2+x+1)\sqrt[3] {x+1}-(x^2+2x+1)\sqrt[3] {x+1}$
$(x^3+x^2+x+1-(x^2+2x+1))\sqrt[3] {x+1}=(x^3-x)\sqrt[3] {x+1}$
$(x^3-x)\sqrt[3] {x+1}=(x^2-1)x\sqrt[3] {x+1}=(x+1)x(x-1)\sqrt[3] {x+1}$
