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

The solution to expand-(-3+sin^2(x))^2cos(x)sin(x) is -9cos(x)sin(x)+6sin^3(x)cos(x)-sin^5(x)cos(x)

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

expand

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

- 9 cos (x) sin (x) + 6 sin^{3} (x) cos (x) - sin^{5} (x) cos (x)

Solution steps

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

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

Expand

(- 3 + sin^{2} (x))^{2} : 9 - 6 sin^{2} (x) + sin^{4} (x)

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

Apply the distributive law:

m (a + b + c) = ma + mb + m c

- cos (x) sin (x) (9 - 6 sin^{2} (x) + sin^{4} (x)) = - cos (x) sin (x) \cdot 9 - cos (x) sin (x) (- 6 sin^{2} (x)) - cos (x) sin (x) sin^{4} (x)

= - cos (x) sin (x) \cdot 9 - cos (x) sin (x) (- 6 sin^{2} (x)) - cos (x) sin (x) sin^{4} (x)

Simplify

- cos (x) sin (x) \cdot 9 - cos (x) sin (x) (- 6 sin^{2} (x)) - cos (x) sin (x) sin^{4} (x) : - 9 cos (x) sin (x) + 6 sin^{3} (x) cos (x) - sin^{5} (x) cos (x)

= - 9 cos (x) sin (x) + 6 sin^{3} (x) cos (x) - sin^{5} (x) cos (x)

7 (6 + 2)

7 (7 + y 21)

\frac{2 x + 5}{( x ^{2} + 2 ) ( x + 1 )}

(2 - \frac{x}{2})^{10}

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

What is expand-(-3+sin^2(x))^2cos(x)sin(x) ?
The solution to expand-(-3+sin^2(x))^2cos(x)sin(x) is -9cos(x)sin(x)+6sin^3(x)cos(x)-sin^5(x)cos(x)