What is expand (-3a^3cos^2(x)sin(x))^2 ?

The solution to expand (-3a^3cos^2(x)sin(x))^2 is 9a^6cos^4(x)sin^2(x)

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expand (-3a^3cos^2(x)sin(x))^2

expand

(- 3 a^{3} cos^{2} (x) sin (x))^{2}

9 a^{6} cos^{4} (x) sin^{2} (x)

Solution steps

(- 3 a^{3} cos^{2} (x) sin (x))^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 3 a^{3} cos^{2} (x) sin (x))^{2} = (3 a^{3} cos^{2} (x) sin (x))^{2}

= (3 a^{3} cos^{2} (x) sin (x))^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 3^{2} sin^{2} (x) (a^{3})^{2} (cos^{2} (x))^{2}

(a^{3})^{2} : a^{6}

= 3^{2} a^{6} (cos^{2} (x))^{2} sin^{2} (x)

(cos^{2} (x))^{2} : cos^{4} (x)

= 3^{2} a^{6} cos^{4} (x) sin^{2} (x)

3^{2} = 9

= 9 a^{6} cos^{4} (x) sin^{2} (x)

- \frac{( x - y ) ^{3}}{3}

\frac{1}{x ( x + 4 ) ^{2}}

(x + h) e^{- (x + h)} - x e^{- x}

\frac{3}{s ( s - 2 )}

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

What is expand (-3a^3cos^2(x)sin(x))^2 ?
The solution to expand (-3a^3cos^2(x)sin(x))^2 is 9a^6cos^4(x)sin^2(x)