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

The solution to expand (2cos(x)-2cos(2x))^2 is 4cos^2(x)-8cos(x)cos(2x)+4cos^2(2x)

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

expand

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

4 cos^{2} (x) - 8 cos (x) cos (2 x) + 4 cos^{2} (2 x)

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(2 cos (x))^{2} - 2 \cdot 2 cos (x) \cdot 2 cos (2 x) + (2 cos (2 x))^{2} : 4 cos^{2} (x) - 8 cos (x) cos (2 x) + 4 cos^{2} (2 x)

= 4 cos^{2} (x) - 8 cos (x) cos (2 x) + 4 cos^{2} (2 x)

(2 + 4) (3 - 3)

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

x (x - 5)

- \frac{4 ( - 3 s ^{2} - 24 s - 44 )}{( s ^{2} + 8 s + 20 ) ^{3}}

x^{\frac{1}{2}} (3 x - 3)

What is expand (2cos(x)-2cos(2x))^2 ?
The solution to expand (2cos(x)-2cos(2x))^2 is 4cos^2(x)-8cos(x)cos(2x)+4cos^2(2x)