What is expand 9(xsin(θ)+ycos(θ))^2 ?

The solution to expand 9(xsin(θ)+ycos(θ))^2 is 9y^2cos^2(θ)+9x^2sin^2(θ)+9xysin(2θ)

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expand 9(xsin(θ)+ycos(θ))^2

expand

9 (x sin (θ) + y cos (θ))^{2}

9 y^{2} cos^{2} (θ) + 9 x^{2} sin^{2} (θ) + 9 x y sin (2 θ)

Solution steps

9 (x sin (θ) + y cos (θ))^{2}

Expand

(x sin (θ) + y cos (θ))^{2} : y^{2} cos^{2} (θ) + x^{2} sin^{2} (θ) + x y sin (2 θ)

= 9 (y^{2} cos^{2} (θ) + x^{2} sin^{2} (θ) + x y sin (2 θ))

Apply the distributive law:

m (a + b + c) = ma + mb + m c

9 (y^{2} cos^{2} (θ) + x^{2} sin^{2} (θ) + x y sin (2 θ)) = 9 y^{2} cos^{2} (θ) + 9 x^{2} sin^{2} (θ) + 9 x y sin (2 θ)

= 9 y^{2} cos^{2} (θ) + 9 x^{2} sin^{2} (θ) + 9 x y sin (2 θ)

\frac{( 160 p ^{4} - 7 q ^{9} ) ^{3}}{1000}

\frac{k}{s ( s + 5 )}

(9 x^{2} + 25 y^{2} = 225) \frac{1}{225}

\frac{\partial}{\partial y} ((x) (1 + 2 x y))

(k - \frac{1}{3})^{3}

What is expand 9(xsin(θ)+ycos(θ))^2 ?
The solution to expand 9(xsin(θ)+ycos(θ))^2 is 9y^2cos^2(θ)+9x^2sin^2(θ)+9xysin(2θ)