展开 pi(1-X^2)^2

解答

展开

π (1 - X^{2})^{2}

π X^{4} - 2 π X^{2} + π

求解步骤

π (1 - X^{2})^{2}

(1 - X^{2})^{2} = 1 - 2 X^{2} + X^{4}

= π (X^{4} - 2 X^{2} + 1)

打开括号

= π 1 + π (- 2 X^{2}) + π X^{4}

使用加减运算法则

+ (- a) = - a

= 1 π - 2 π X^{2} + π X^{4}

乘以:

1 π = π

= π - 2 π X^{2} + π X^{4}

改写为标准形式

= π X^{4} - 2 π X^{2} + π

e x p an d (x + 1 - x^{2})^{5}

e x p an d 1 n (x^{\frac{2}{5}} y^{\frac{4}{3}})

e x p an d \frac{- 3 y ^{3} - 6 x ^{2} y}{x ( 2 x ^{2} + 9 y ^{2} )}

e x p an d \frac{1 - cot ^{4} ( x )}{csc ^{2} ( x ) ( sin ( x ) + cos ( x ) )}

e x p an d \frac{x ^{2} + 2 x - 2}{( x - 1 ) ( x ^{2} - 4 x + 2 )}