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

The solution to expand (2tcos(t)-t^2sin(t))^2 is 4t^2cos^2(t)-4t^3cos(t)sin(t)+t^4sin^2(t)

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(2 t cos (t))^{2} - 2 \cdot 2 t cos (t) t^{2} sin (t) + (t^{2} sin (t))^{2} : 4 t^{2} cos^{2} (t) - 4 t^{3} cos (t) sin (t) + t^{4} sin^{2} (t)

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

\frac{x}{4} y \frac{3}{8}

(5 x + 5)^{3}

\frac{9}{10} - \frac{7}{8}

\frac{1}{2} \times 2

45!

What is expand (2tcos(t)-t^2sin(t))^2 ?
The solution to expand (2tcos(t)-t^2sin(t))^2 is 4t^2cos^2(t)-4t^3cos(t)sin(t)+t^4sin^2(t)