What is expand (2cos(t)-tsin(t))^2 ?

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

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expand (2cos(t)-tsin(t))^2

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{4}{16} x + \frac{5}{16} y + \frac{3}{16} z + \frac{4}{16} u

(x + 7 - 2) (x + 7 + 2)

(3 + 2) (1 - 3)

(2 e^{t} + 5) (e^{t})

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