What is expand (-vsin^2(u)-vcos^2(u))^2 ?

The solution to expand (-vsin^2(u)-vcos^2(u))^2 is v^2sin^4(u)+2v^2sin^2(u)cos^2(u)+v^2cos^4(u)

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expand (-vsin^2(u)-vcos^2(u))^2

expand

(- v sin^{2} (u) - v cos^{2} (u))^{2}

v^{2} sin^{4} (u) + 2 v^{2} sin^{2} (u) cos^{2} (u) + v^{2} cos^{4} (u)

Solution steps

(- v sin^{2} (u) - v cos^{2} (u))^{2}

Apply Perfect Square Formula:

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

(- v sin^{2} (u) - v cos^{2} (u))^{2} = (- v sin^{2} (u))^{2} - 2 (- v sin^{2} (u)) v cos^{2} (u) + (v cos^{2} (u))^{2}

= (- v sin^{2} (u))^{2} - 2 (- v sin^{2} (u)) v cos^{2} (u) + (v cos^{2} (u))^{2}

Simplify

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

= v^{2} sin^{4} (u) + 2 v^{2} sin^{2} (u) cos^{2} (u) + v^{2} cos^{4} (u)

(t + 2 t)^{4}

3 y^{2} (6 - 3 y) - \frac{1}{6} y (6 - 3 y)^{3} - \frac{3}{2} y^{3} (6 - 3 y)

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

343 \cdot 63

(\frac{2 m}{3} + 7 b) (\frac{2 m}{3} - 7 b)

What is expand (-vsin^2(u)-vcos^2(u))^2 ?
The solution to expand (-vsin^2(u)-vcos^2(u))^2 is v^2sin^4(u)+2v^2sin^2(u)cos^2(u)+v^2cos^4(u)