展开 ((x^2+x)/x)^2

解答

展开

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

x^{2} + 2 x + 1

求解步骤

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

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

= (x + 1)^{2}

使用完全平方公式:

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

a = x, b = 1

= x^{2} + 2 x \cdot 1 + 1^{2}

化简

x^{2} + 2 x \cdot 1 + 1^{2} : x^{2} + 2 x + 1

= x^{2} + 2 x + 1

e x p an d e^{x} (e^{2} x + 1)^{3}

e x p an d \frac{2}{( x ^{2} + 1 ) ^{2}}

e x p an d \frac{5 x ^{2} - 16 x + 2}{3 x ( x - 1 )}

e x p an d - \frac{u}{( u - 1 ) ^{2}}

e x p an d y^{'} (x) - (y^{2} + 1) sin (x)