What is expand (3+3cos(θ))^3 ?

The solution to expand (3+3cos(θ))^3 is 27+81cos(θ)+81cos^2(θ)+27cos^3(θ)

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expand (3+3cos(θ))^3

expand

(3 + 3 cos (θ))^{3}

27 + 81 cos (θ) + 81 cos^{2} (θ) + 27 cos^{3} (θ)

Solution steps

(3 + 3 cos (θ))^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(3 + 3 cos (θ))^{3} = 3^{3} + 3 \cdot 3^{2} \cdot 3 cos (θ) + 3 \cdot 3 (3 cos (θ))^{2} + (3 cos (θ))^{3}

= 3^{3} + 3 \cdot 3^{2} \cdot 3 cos (θ) + 3 \cdot 3 (3 cos (θ))^{2} + (3 cos (θ))^{3}

Simplify

3^{3} + 3 \cdot 3^{2} \cdot 3 cos (θ) + 3 \cdot 3 (3 cos (θ))^{2} + (3 cos (θ))^{3} : 27 + 81 cos (θ) + 81 cos^{2} (θ) + 27 cos^{3} (θ)

= 27 + 81 cos (θ) + 81 cos^{2} (θ) + 27 cos^{3} (θ)

(2 - x + 2) (2 + x + 2)

(2 + 2 i)^{5}

(9 + sec (θ)) sin (θ)

\frac{7 x + 3}{( x + 4 ) ( x - 1 )}

(a - b) \frac{a + b}{a - b} - (a + b) \frac{a - b}{a + b} + (2 a - 2 b) \frac{1}{a - b}

What is expand (3+3cos(θ))^3 ?
The solution to expand (3+3cos(θ))^3 is 27+81cos(θ)+81cos^2(θ)+27cos^3(θ)