What is expand (8xy^3+1)*(18sin^8(t)cos(t)) ?

The solution to expand (8xy^3+1)*(18sin^8(t)cos(t)) is 144xsin^8(t)y^3cos(t)+18sin^8(t)cos(t)

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expand (8xy^3+1)*(18sin^8(t)cos(t))

expand

(8 x y^{3} + 1) \cdot (18 sin^{8} (t) cos (t))

144 x sin^{8} (t) y^{3} cos (t) + 18 sin^{8} (t) cos (t)

Solution steps

(8 x y^{3} + 1) (18 sin^{8} (t) cos (t))

= (18 sin^{8} (t) cos (t)) (8 x y^{3} + 1)

Apply the distributive law:

a (b + c) = ab + a c

(18 sin^{8} (t) cos (t)) (8 x y^{3} + 1) = 18 sin^{8} (t) cos (t) \cdot 8 x y^{3} + 18 sin^{8} (t) cos (t) \cdot 1

= 18 sin^{8} (t) cos (t) \cdot 8 x y^{3} + 18 sin^{8} (t) cos (t) \cdot 1

Simplify

18 sin^{8} (t) cos (t) \cdot 8 x y^{3} + 18 sin^{8} (t) cos (t) \cdot 1 : 144 x sin^{8} (t) y^{3} cos (t) + 18 sin^{8} (t) cos (t)

= 144 x sin^{8} (t) y^{3} cos (t) + 18 sin^{8} (t) cos (t)

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- 10 sin (t) (5 sin (t) - 3) + 25 cos (t) (5 cos (t) + 1)

What is expand (8xy^3+1)*(18sin^8(t)cos(t)) ?
The solution to expand (8xy^3+1)*(18sin^8(t)cos(t)) is 144xsin^8(t)y^3cos(t)+18sin^8(t)cos(t)