What is expand (xcos(θ)+y)^2-x^2sin^2(θ) ?

The solution to expand (xcos(θ)+y)^2-x^2sin^2(θ) is x^2cos^2(θ)+2xycos(θ)+y^2-x^2sin^2(θ)

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expand (xcos(θ)+y)^2-x^2sin^2(θ)

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} ((y) (2 x - 3 y)^{3})

e^{2 x} (e^{x} + 1)

- 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

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

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

What is expand (xcos(θ)+y)^2-x^2sin^2(θ) ?
The solution to expand (xcos(θ)+y)^2-x^2sin^2(θ) is x^2cos^2(θ)+2xycos(θ)+y^2-x^2sin^2(θ)