Докажите, что: (x^2+1)^2-4x^2=(x-1)^2(x+1)^2.

Ответ:

\[\left( x^{2} + 1 \right)^{2} - 4x^{2} = (x - 1)^{2}(x + 1)^{2}\]

\[\left( x^{2} + 1 \right)^{2} - 4x^{2} = (x - 1)^{2}(x + 1)^{2}\ \]

\[\left( x^{2} + 1 - 2x \right)\left( x^{2} + 1 + 2x \right) =\]

\[= (x - 1)^{2}(x + 1)^{2}\]

\[\left( x^{2} - 2x + 1 \right)\left( x^{2} + 2x + 1 \right) =\]

\[= (x - 1)^{2}(x + 1)^{2}\]

\[(x - 1)^{2}(x + 1)^{2} = (x - 1)^{2}(x + 1)^{2}\]

\[Что\ и\ требовалось\ доказать.\]