展开 (1-(x^2)/2)^2

解答

展开

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

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

求解步骤

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

使用完全平方公式:

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

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

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

化简

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

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

s im pl i f y (2 p + \frac{3}{4}) (2 p - \frac{3}{4})

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

s im pl i f y (1 - \frac{3}{3}) \cdot (1 + \frac{3}{3})

e x p an d 5 l e f t (4 - a + 3 x) + (2 + a - x)

s im pl i f y 2 (2 + 10)