What is expand (1-cos^2(x))^3 ?

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

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expand (1-cos^2(x))^3

expand

(1 - cos^{2} (x))^{3}

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

Solution steps

(1 - cos^{2} (x))^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

(cos (x) - 1) (sin (x) - 1)

\frac{1}{s ( s + 3 )}

x (x - 3 x)

(2 + \frac{1}{4} x)^{8}

\frac{2 x y}{( x + 3 ) ( x - 8 )}

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