What is expand ((1-cos(x))^3cos^2(x))/3 ?

The solution to expand ((1-cos(x))^3cos^2(x))/3 is (cos^2(x))/3-cos^3(x)+cos^4(x)-(cos^5(x))/3

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expand ((1-cos(x))^3cos^2(x))/3

expand

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

\frac{cos ^{2} ( x )}{3} - cos^{3} (x) + cos^{4} (x) - \frac{cos ^{5} ( x )}{3}

Solution steps

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

(1 - cos (x))^{3} = 1 - 3 cos (x) + 3 cos^{2} (x) - cos^{3} (x)

= \frac{cos ^{2} ( x ) ( 3 cos ^{2} ( x ) - cos ^{3} ( x ) - 3 cos ( x ) + 1 )}{3}

Expand

(1 - 3 cos (x) + 3 cos^{2} (x) - cos^{3} (x)) cos^{2} (x) : cos^{2} (x) - 3 cos^{3} (x) + 3 cos^{4} (x) - cos^{5} (x)

= \frac{cos ^{2} ( x ) - 3 cos ^{3} ( x ) + 3 cos ^{4} ( x ) - cos ^{5} ( x )}{3}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{cos ^{2} ( x ) - 3 cos ^{3} ( x ) + 3 cos ^{4} ( x ) - cos ^{5} ( x )}{3} = \frac{cos ^{2} ( x )}{3} - \frac{3 cos ^{3} ( x )}{3} + \frac{3 cos ^{4} ( x )}{3} - \frac{cos ^{5} ( x )}{3}

= \frac{cos ^{2} ( x )}{3} - \frac{3 cos ^{3} ( x )}{3} + \frac{3 cos ^{4} ( x )}{3} - \frac{cos ^{5} ( x )}{3}

Divide the numbers:

\frac{3}{3} = 1

= \frac{cos ^{2} ( x )}{3} - cos^{3} (x) + cos^{4} (x) - \frac{cos ^{5} ( x )}{3}

\frac{1}{3} (e^{- x} + 2)

\frac{( 9 s + 47 )}{( s - 3 ) ( s - 8 )}

(\frac{1}{2 x} - \frac{1}{2 x ^{\frac{3}{2}}}) (x - 4)

(- y + 2) (x + \frac{5}{2}) - (y + 1) (- x - \frac{1}{2})

(4 + 3 x) x^{3} + e^{3 x} \cdot 3 x^{4} + 4

What is expand ((1-cos(x))^3cos^2(x))/3 ?
The solution to expand ((1-cos(x))^3cos^2(x))/3 is (cos^2(x))/3-cos^3(x)+cos^4(x)-(cos^5(x))/3