展开 1/15 cos^3(x)(3cos^2(x)-5)

解答

展开

\frac{1}{15} cos^{3} (x) (3 cos^{2} (x) - 5)

\frac{cos ^{5} ( x )}{5} - \frac{cos ^{3} ( x )}{3}

求解步骤

\frac{1}{15} cos^{3} (x) (3 cos^{2} (x) - 5)

使用分配律:

a (b - c) = ab - a c

\frac{1}{15} cos^{3} (x) (3 cos^{2} (x) - 5) = \frac{1}{15} cos^{3} (x) \cdot 3 cos^{2} (x) - \frac{1}{15} cos^{3} (x) \cdot 5

= \frac{1}{15} cos^{3} (x) \cdot 3 cos^{2} (x) - \frac{1}{15} cos^{3} (x) \cdot 5

化简

\frac{1}{15} cos^{3} (x) \cdot 3 cos^{2} (x) - \frac{1}{15} cos^{3} (x) \cdot 5 : \frac{cos ^{5} ( x )}{5} - \frac{cos ^{3} ( x )}{3}

= \frac{cos ^{5} ( x )}{5} - \frac{cos ^{3} ( x )}{3}

s im pl i f y (s + 2 + 23 j) (s + 2 - 23 j) (s + 12)

s im pl i f y (x - 5) \cdot (3 x + 6)

e x p an d (10 - 2) 3 + 5

e x p an d (1 + cos (t)) cos (\frac{t}{2}) + sin (t) sin (\frac{t}{2})

e x p an d (5 sec (θ) + 2)^{2}