What is expand (-2sin(t)-tcos(t))^2 ?

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

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expand (-2sin(t)-tcos(t))^2

expand

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

4 sin^{2} (t) + 4 t cos (t) sin (t) + t^{2} cos^{2} (t)

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

= 4 sin^{2} (t) + 4 t cos (t) sin (t) + t^{2} cos^{2} (t)

(x - 1 + i y)^{2}

\frac{- 2 x ^{2} - 22 x - 2}{3 ( x - 2 ) ( x + 1 ) ( x - 5 )}

(x + \frac{7}{2})^{2}

e^{y + C} ∣ y ∣^{3} (4 - 4 x + y)

(x^{2} y + x) \frac{d y}{d x} + (x y^{2} - y)

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