What is expand (1-cos^2(θ))^3 ?

The solution to expand (1-cos^2(θ))^3 is 1-3cos^2(θ)+3cos^4(θ)-cos^6(θ)

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expand (1-cos^2(θ))^3

expand

(1 - cos^{2} (θ))^{3}

1 - 3 cos^{2} (θ) + 3 cos^{4} (θ) - cos^{6} (θ)

Solution steps

(1 - cos^{2} (θ))^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

1^{3} - 3 \cdot 1^{2} cos^{2} (θ) + 3 \cdot 1 \cdot (cos^{2} (θ))^{2} - (cos^{2} (θ))^{3} : 1 - 3 cos^{2} (θ) + 3 cos^{4} (θ) - cos^{6} (θ)

= 1 - 3 cos^{2} (θ) + 3 cos^{4} (θ) - cos^{6} (θ)

(x + 12) (x - \frac{7}{5})

x (1 - cos (x))

y (3 x^{2} - y^{2}) d x + x^{3} d y

e^{(- 2 - i) x}

\frac{0.82585}{( 1 + 0.088582 S ) ( 1 + 0.014589 S )}

What is expand (1-cos^2(θ))^3 ?
The solution to expand (1-cos^2(θ))^3 is 1-3cos^2(θ)+3cos^4(θ)-cos^6(θ)