Question

Factor x^4 + x y^3 + x^3 + y^3 completely. Show your work.

Answer 1

$\bf x^4+xy^3+x^3+y^3\impliedby \textit{now let's do some grouping} \\\\\\ (x^4+xy^3)~~+~~(x^3+y^3)\implies x(x^3+y^3)~~+~~(x^3+y^3) \\\\\\ \stackrel{\stackrel{common}{factor}}{(x^3+y^3)}(x+1)\\\\ -------------------------------\\\\ \textit{now recall that }\qquad \qquad \textit{difference of cubes} \\ \quad \\ a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad a^3-b^3 = (a-b)(a^2+ab+b^2)\\\\ -------------------------------\\\\ (x+y)(x^2-xy+y^2)(x+1)$