Question

(X−1)^2+(X−1)^3 e equivalente a?

Answer 1

$(x-1)^{2}+(x-1)^{3}=1\cdot(x-1)^{2}+(x-1)^{2}\cdot(x-1)^{1}\\\\(x-1)^{2}+(x-1)^{3}=1\cdot(x-1)^{2}+(x-1)^{2}\cdot(x-1)$

Colocando (x - 1)² em evidência:

$(x-1)^{2}+(x-1)^{3}=(x-1)^{2}\cdot[1+(x-1)]\\\\\\(x-1)^{2}+(x-1)^{3}=(x-1)^{2}(1+x-1)\\\\\\\boxed{\boxed{(x-1)^{2}+(x-1)^{3}=x(x-1)^{2}}}$

Se quiser, podemos expandir o quadrado da diferença:

$(x-1)^{2}+(x-1)^{3}=x\cdot(x^{2}-2\cdot x\cdot1+1^{2})\\\\(x-1)^{2}+(x-1)^{3}=x\cdot(x^{2}-2x+1)\\\\\boxed{\boxed{(x-1)^{2}+(x-1)^{3}=x^{3}-2x^{2}+x}}$