展开 (cos^2(x)-2)^2

解答

展开

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

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

求解步骤

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

使用完全平方公式:

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

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

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

化简

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

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

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

s im pl i f y (53 - 82) \cdot (- 7)

e x p an d (f (x) = 1, - 2 x \cdot g (x) = 2 x^{2} - 1) \cdot x

e x p an d \frac{- 5 x ^{2} - 32 x + 80}{( x ^{2} - 5 x ) ^{2}}

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