Question

How to factor 4(x+5)^3(x-1)^2-(x+5)^4 • 2 (x-1) by grouping?

Answer 1

$\bf 4(x+5)^3(x-1)^2-(x+5)^4\cdot 2(x-1) \\\\\\ 4(x+5)^3(x-1)^2-2(x-1)(x+5)^4 \\\\\\ \underline{2}\cdot 2\underline{(x+5)^3}(x-1)\underline{(x-1)}~-~\underline{2}\underline{(x-1)}(x+5)\underline{(x+5)^3}\leftarrow \begin{array}{llll} notice~the\\ common\\ \underline{factors} \end{array} \\\\\\ 2(x+5)^3(x-1)~[~2(x-1)-(x+5)~] \\\\\\ 2(x+5)^3(x-1)~[2x-2-x-5]\implies 2(x+5)^3(x-1)(x-7)$