expand (x-1/x)^2

פתרון

expand

(x - \frac{1}{x})^{2}

\frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}}

צעדי פתרון

(x - \frac{1}{x})^{2}

(a - b)^{2} = a^{2} - 2 ab + b^{2}

:הפעל נוסחת הכפל המקוצר

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

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

x^{2} - 2 x \frac{1}{x} + (\frac{1}{x})^{2}

פשט את:

\frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}}

= \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}}

\frac{1}{x ^{2} ( x - 2 )}

- \frac{2 x}{( x ^{2} + 1 ) ^{2}}

(T - b) (T - c) (T - d) (T - e) (T - f)

(3 - i)^{10}