展开 (1-(t^2)/2+(t^4)/(24))^2

解答

展开

(1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{24})^{2}

1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{3} - \frac{t ^{2}}{2} - \frac{t ^{6}}{48} - \frac{t ^{6}}{48} + \frac{t ^{8}}{576}

求解步骤

(1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{24})^{2}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{24})^{2} = (1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{24}) (1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{24})

= (1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{24}) (1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{24})

打开括号

= 1 \cdot 1 + 1 \cdot (- \frac{t ^{2}}{2}) + 1 \cdot \frac{t ^{4}}{24} - \frac{t ^{2}}{2} \cdot 1 - \frac{t ^{2}}{2} (- \frac{t ^{2}}{2}) - \frac{t ^{2}}{2} \cdot \frac{t ^{4}}{24} + \frac{t ^{4}}{24} \cdot 1 + \frac{t ^{4}}{24} (- \frac{t ^{2}}{2}) + \frac{t ^{4}}{24} \cdot \frac{t ^{4}}{24}

化简

1 \cdot 1 + 1 \cdot (- \frac{t ^{2}}{2}) + 1 \cdot \frac{t ^{4}}{24} - \frac{t ^{2}}{2} \cdot 1 - \frac{t ^{2}}{2} (- \frac{t ^{2}}{2}) - \frac{t ^{2}}{2} \cdot \frac{t ^{4}}{24} + \frac{t ^{4}}{24} \cdot 1 + \frac{t ^{4}}{24} (- \frac{t ^{2}}{2}) + \frac{t ^{4}}{24} \cdot \frac{t ^{4}}{24} : 1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{3} - \frac{t ^{2}}{2} - \frac{t ^{6}}{48} - \frac{t ^{6}}{48} + \frac{t ^{8}}{576}

= 1 - \frac{t ^{2}}{2} + \frac{t ^{4}}{3} - \frac{t ^{2}}{2} - \frac{t ^{6}}{48} - \frac{t ^{6}}{48} + \frac{t ^{8}}{576}

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