What is expand (2ye^{xy}+xe^{xy})^2 ?

The solution to expand (2ye^{xy}+xe^{xy})^2 is 4e^{2yx}y^2+4e^{2yx}yx+e^{2yx}x^2

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expand (2ye^{xy}+xe^{xy})^2

expand

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

4 e^{2 y x} y^{2} + 4 e^{2 y x} y x + e^{2 y x} x^{2}

Solution steps

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

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

Apply Perfect Square Formula:

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

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

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

Simplify

(2 y e^{x y})^{2} + 2 \cdot 2 y e^{x y} x e^{x y} + (x e^{x y})^{2} : 4 e^{2 y x} y^{2} + 4 e^{2 y x} y x + e^{2 y x} x^{2}

= 4 e^{2 y x} y^{2} + 4 e^{2 y x} y x + e^{2 y x} x^{2}

(1 + cos (x) + i sin (x))^{2}

- 7 (5 x + 42 y = - 69)

tan^{2} (x) (cot^{2} (x) - cos^{2} (x))

\frac{1}{x \cdot ( x - 1 )}

(4 - \frac{x}{3})^{5}

What is expand (2ye^{xy}+xe^{xy})^2 ?
The solution to expand (2ye^{xy}+xe^{xy})^2 is 4e^{2yx}y^2+4e^{2yx}yx+e^{2yx}x^2