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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

((- 3 sin (t)) + 4 cos (t) - 2 t) (1 - t^{2})

\frac{x ^{2} - x + 9}{( x ^{2} + 9 ) ^{2}}

(53 - 82) \cdot (- 7)

(f (x) = 1, - 2 x \cdot g (x) = 2 x^{2} - 1) \cdot x

\frac{- 5 x ^{2} - 32 x + 80}{( x ^{2} - 5 x ) ^{2}}

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