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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(12) (8) (- 8) (- 12)

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

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

2 (e^{4} - e^{2}) - 12

t (x) x^{^{''}} - (t (x) + 2) x^{^{'}} + 2 x

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