展開する (1-(pi^2l^2)/(16))^2

解

展開する

(1 - \frac{π ^{2} l ^{2}}{16})^{2}

1 - \frac{π ^{2} l ^{2}}{8} + \frac{π ^{4} l ^{4}}{256}

解答ステップ

(1 - \frac{π ^{2} l ^{2}}{16})^{2}

完全平方式を適用する:

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

a = 1, b = \frac{π ^{2} l ^{2}}{16}

= 1^{2} - 2 \cdot 1 \cdot \frac{π ^{2} l ^{2}}{16} + (\frac{π ^{2} l ^{2}}{16})^{2}

簡素化

1^{2} - 2 \cdot 1 \cdot \frac{π ^{2} l ^{2}}{16} + (\frac{π ^{2} l ^{2}}{16})^{2} : 1 - \frac{π ^{2} l ^{2}}{8} + \frac{π ^{4} l ^{4}}{256}

= 1 - \frac{π ^{2} l ^{2}}{8} + \frac{π ^{4} l ^{4}}{256}