What is expand (1+cos(θ))^3 ?

The solution to expand (1+cos(θ))^3 is 1+3cos(θ)+3cos^2(θ)+cos^3(θ)

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expand (1+cos(θ))^3

expand

(1 + cos (θ))^{3}

1 + 3 cos (θ) + 3 cos^{2} (θ) + cos^{3} (θ)

Solution steps

(1 + cos (θ))^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

1^{3} + 3 \cdot 1^{2} cos (θ) + 3 \cdot 1 \cdot cos^{2} (θ) + cos^{3} (θ) : 1 + 3 cos (θ) + 3 cos^{2} (θ) + cos^{3} (θ)

= 1 + 3 cos (θ) + 3 cos^{2} (θ) + cos^{3} (θ)

\frac{- 4 x ^{2} + 4}{( x ^{2} + 1 ) ^{2}}

(- \frac{x ^{3}}{4} + 2 y) (3 x^{2} - x y + y^{4})

(8 x + \frac{1}{2 x})^{8}

\frac{3 s + 1}{( s + 4 ) ^{3} ( s ^{2} + s + 2.5 )}

What is expand (1+cos(θ))^3 ?
The solution to expand (1+cos(θ))^3 is 1+3cos(θ)+3cos^2(θ)+cos^3(θ)