展开 (1+pi/2)(pi-pi/2)

解答

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(1 + \frac{π}{2}) (π - \frac{π}{2})

\frac{π ^{2}}{4} + \frac{π}{2}

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4.03819 \dots

求解步骤

(1 + \frac{π}{2}) (π - \frac{π}{2})

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = 1, b = \frac{π}{2}, c = π, d = - \frac{π}{2}

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

使用加减运算法则

+ (- a) = - a

= 1 π - 1 \cdot \frac{π}{2} + π \frac{π}{2} - \frac{π}{2} \cdot \frac{π}{2}

化简

1 π - 1 \cdot \frac{π}{2} + π \frac{π}{2} - \frac{π}{2} \cdot \frac{π}{2} : \frac{π ^{2}}{4} + \frac{π}{2}

= \frac{π ^{2}}{4} + \frac{π}{2}

e x p an d 2 (22500 ln (1968300000000) - 200)

e x p an d \frac{( 4 - x ^{2} ) ^{3}}{8 x ^{3}}

\frac{d ^{2}}{d x ^{2}} ((y) (- 6 x^{4} + 9))

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

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