What is expand (1+sin^3(t))(3sin^2(t)cos(t)) ?

The solution to expand (1+sin^3(t))(3sin^2(t)cos(t)) is 3sin^2(t)cos(t)+3sin^5(t)cos(t)

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expand (1+sin^3(t))(3sin^2(t)cos(t))

expand

(1 + sin^{3} (t)) (3 sin^{2} (t) cos (t))

3 sin^{2} (t) cos (t) + 3 sin^{5} (t) cos (t)

Solution steps

(1 + sin^{3} (t)) (3 sin^{2} (t) cos (t))

= (3 sin^{2} (t) cos (t)) (1 + sin^{3} (t))

Apply the distributive law:

a (b + c) = ab + a c

(3 sin^{2} (t) cos (t)) (1 + sin^{3} (t)) = 3 sin^{2} (t) cos (t) \cdot 1 + 3 sin^{2} (t) cos (t) sin^{3} (t)

= 3 sin^{2} (t) cos (t) \cdot 1 + 3 sin^{2} (t) cos (t) sin^{3} (t)

Simplify

3 sin^{2} (t) cos (t) \cdot 1 + 3 sin^{2} (t) cos (t) sin^{3} (t) : 3 sin^{2} (t) cos (t) + 3 sin^{5} (t) cos (t)

= 3 sin^{2} (t) cos (t) + 3 sin^{5} (t) cos (t)

\frac{sin ^{2} ( ( x + 2 ) ( x - 2 ) )}{( x + 2 ) ( x - 2 )}

(x^{2} + 1) x

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

(1 + sin (x)) (1 - cos (x))

50 (1 - e^{2})

What is expand (1+sin^3(t))(3sin^2(t)cos(t)) ?
The solution to expand (1+sin^3(t))(3sin^2(t)cos(t)) is 3sin^2(t)cos(t)+3sin^5(t)cos(t)