展开 (1/x+2)^2

解答

展开

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

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

求解步骤

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

使用完全平方公式:

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

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

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

化简

(\frac{1}{x})^{2} + 2 \cdot \frac{1}{x} \cdot 2 + 2^{2} : \frac{4 x ^{2} + 1 + 4 x}{x ^{2}}

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

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