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受欢迎的代数 >

展开 (1-cos^2(x))^4

解答

展开

(1 - cos^{2} (x))^{4}

解答

1 - 4 cos^{2} (x) + 6 cos^{4} (x) - 4 cos^{6} (x) + cos^{8} (x)

求解步骤

(1 - cos^{2} (x))^{4}

使用二项式定理:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 1, b = - cos^{2} (x)

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (- cos^{2} (x))^{i}

展开求和

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (- cos^{2} (x))^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (- cos^{2} (x))^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (- cos^{2} (x))^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (- cos^{2} (x))^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- cos^{2} (x))^{4}

化简

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (- cos^{2} (x))^{0} : 1

化简

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (- cos^{2} (x))^{1} : - 4 cos^{2} (x)

化简

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (- cos^{2} (x))^{2} : 6 cos^{4} (x)

化简

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (- cos^{2} (x))^{3} : - 4 cos^{6} (x)

化简

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- cos^{2} (x))^{4} : cos^{8} (x)

= 1 - 4 cos^{2} (x) + 6 cos^{4} (x) - 4 cos^{6} (x) + cos^{8} (x)

流行的例子

化简 1/2 (1-cos(x))

s im pl i f y \frac{1}{2} (1 - cos (x))

展开 (5x+2y=8,)(2x-4y=-8)

e x p an d (5 x + 2 y = 8,) (2 x - 4 y = - 8)

展开 (e^x-e^{-x})^4

e x p an d (e^{x} - e^{- x})^{4}

展开 A(-3,-2)yB(8,3)

e x p an d A (- 3, - 2) y B (8, 3)

展开 ((1+4x)^{-1/2})^3

e x p an d ((1 + 4 x)^{- \frac{1}{2}})^{3}