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

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

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

expand

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

- 4 sin (2 x) + 4

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

= 4 (- sin (2 x) + 1)

Apply the distributive law:

a (b + c) = ab + a c

4 (- sin (2 x) + 1) = 4 (- sin (2 x)) + 4 \cdot 1

= 4 (- sin (2 x)) + 4 \cdot 1

Simplify

4 (- sin (2 x)) + 4 \cdot 1 : - 4 sin (2 x) + 4

= - 4 sin (2 x) + 4

\frac{s - e ^{- \frac{s π}{2}} + 1}{s ( s ^{2} + 1 )}

(x^{2} + 5 x + 6) (\frac{1}{2} sin (2 x))

\frac{\partial}{\partial x} ((z) (4 x yz - e^{z}))

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

\frac{7 + 2 s + 6 e ^{- 4 s}}{( s + 2 ) ( s + 6 )}

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