What is expand (sin(x)+1)(sin(x)-1)(4sin(x)+1) ?

The solution to expand (sin(x)+1)(sin(x)-1)(4sin(x)+1) is -4cos^2(x)sin(x)-cos^2(x)

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expand (sin(x)+1)(sin(x)-1)(4sin(x)+1)

expand

(sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

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

Solution steps

(sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

Expand

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

= - cos^{2} (x) (4 sin (x) + 1)

Apply the distributive law:

a (b + c) = ab + a c

- cos^{2} (x) (4 sin (x) + 1) = - cos^{2} (x) \cdot 4 sin (x) - cos^{2} (x) \cdot 1

= - cos^{2} (x) \cdot 4 sin (x) - cos^{2} (x) \cdot 1

Simplify

- cos^{2} (x) \cdot 4 sin (x) - cos^{2} (x) \cdot 1 : - 4 cos^{2} (x) sin (x) - cos^{2} (x)

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

- 6 (e^{x} - e^{2 x})

x^{\frac{4}{5}} \times (x - 4)^{2}

\frac{e ^{- t} t ^{2} ( 14 + 2 t )}{9} + 15 - 10 t

(\frac{3 x ^{3}}{2} + 9 y^{2}) (\frac{3 x ^{3}}{2} - 9 y^{2})

(x + 1) (x - 4) (x - 2)

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