What is expand (sqrt(2)cos(t)-sqrt(2)-sqrt(2)sin(t))^2 ?

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

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expand (sqrt(2)cos(t)-sqrt(2)-sqrt(2)sin(t))^2

expand

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

4 sin (t) - 4 cos (t) - 2 sin (2 t) + 4

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(2 cos (t) - 2 - 2 sin (t))^{2} = (2 cos (t) - 2 - 2 sin (t)) (2 cos (t) - 2 - 2 sin (t))

= (2 cos (t) - 2 - 2 sin (t)) (2 cos (t) - 2 - 2 sin (t))

Distribute parentheses

= 2 cos (t) 2 cos (t) + 2 cos (t) (- 2) + 2 cos (t) (- 2 sin (t)) - 22 cos (t) - 2 (- 2) - 2 (- 2 sin (t)) - 2 sin (t) 2 cos (t) - 2 sin (t) (- 2) - 2 sin (t) (- 2 sin (t))

Simplify

2 cos (t) 2 cos (t) + 2 cos (t) (- 2) + 2 cos (t) (- 2 sin (t)) - 22 cos (t) - 2 (- 2) - 2 (- 2 sin (t)) - 2 sin (t) 2 cos (t) - 2 sin (t) (- 2) - 2 sin (t) (- 2 sin (t)) : 4 sin (t) - 4 cos (t) - 2 sin (2 t) + 4

= 4 sin (t) - 4 cos (t) - 2 sin (2 t) + 4

{(5 + 3 e^{- 2 t})^{2}} (s)

(x - 8) (x - \frac{1}{2})

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

\frac{x - 1}{( x - 5 ) ^{2}}

\frac{1}{( 1 + t ^{2} ) ( t ^{2} + s ^{2} )}

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