What is expand (x+e^{x/2}y)^2 ?

The solution to expand (x+e^{x/2}y)^2 is x^2+2e^{x/2}xy+e^xy^2

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expand (x+e^{x/2}y)^2

expand

(x + e^{\frac{x}{2}} y)^{2}

x^{2} + 2 e^{\frac{x}{2}} x y + e^{x} y^{2}

Solution steps

(x + e^{\frac{x}{2}} y)^{2}

Apply Perfect Square Formula:

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

a = x, b = e^{\frac{x}{2}} y

= x^{2} + 2 x e^{\frac{x}{2}} y + (e^{\frac{x}{2}} y)^{2}

(e^{\frac{x}{2}} y)^{2} = e^{x} y^{2}

= x^{2} + 2 e^{\frac{x}{2}} x y + e^{x} y^{2}

\frac{1}{( cos ( θ ) + i sin ( θ ) ) ^{2}}

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What is expand (x+e^{x/2}y)^2 ?
The solution to expand (x+e^{x/2}y)^2 is x^2+2e^{x/2}xy+e^xy^2