What is expand (1+5sin^2(t))(5sin(2t)) ?

The solution to expand (1+5sin^2(t))(5sin(2t)) is 5sin(2t)+25sin^2(t)sin(2t)

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expand (1+5sin^2(t))(5sin(2t))

expand

(1 + 5 sin^{2} (t)) (5 sin (2 t))

5 sin (2 t) + 25 sin^{2} (t) sin (2 t)

Solution steps

(1 + 5 sin^{2} (t)) (5 sin (2 t))

= (5 sin (2 t)) (1 + 5 sin^{2} (t))

Apply the distributive law:

a (b + c) = ab + a c

(5 sin (2 t)) (1 + 5 sin^{2} (t)) = 5 sin (2 t) \cdot 1 + 5 sin (2 t) \cdot 5 sin^{2} (t)

= 5 sin (2 t) \cdot 1 + 5 sin (2 t) \cdot 5 sin^{2} (t)

Simplify

5 sin (2 t) \cdot 1 + 5 sin (2 t) \cdot 5 sin^{2} (t) : 5 sin (2 t) + 25 sin^{2} (t) sin (2 t)

= 5 sin (2 t) + 25 sin^{2} (t) sin (2 t)

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

\frac{i 2 ^{k - 2} ( ( - ia ) ^{k} - ( ia ) ^{k} )}{a}

\frac{z ( 65 a ^{3} b ^{5} - 174 c ^{2} x )}{1885 a ^{2} b ^{3} c}

\frac{( x ^{2} - 16 ) ( x ^{2} + 6 x + 8 )}{( x - 1 ) ( x ^{2} + 2 x - 3 )}

\frac{d ^{2} y}{d ^{2} x} (x^{2} + y^{2} = 25)

What is expand (1+5sin^2(t))(5sin(2t)) ?
The solution to expand (1+5sin^2(t))(5sin(2t)) is 5sin(2t)+25sin^2(t)sin(2t)