Question

calculati: x(la puterea)3 -3x(la puterea) 2 +3x - 1

Answer 1

$x^3-3x^2+3x-1 \iff x^3-x^2-2x^2+2x+x-1 \\\\ \iff x^2(x-1)-2x(x-1)+(x-1) \iff \\\\ \iff \underline{(x-1)(x^2-2x+1)} \iff \\\\ \iff (x-1)(x^2-x-x+1) \iff \\\\ \iff(x-1)[x(x-1)-(x-1)] \iff \\\\ \iff(x-1)(x-1)(x-1) \longrightarrow \underline{(x-1)^3}$