What is expand-2(1+a^{1/2}x+ay)^2 ?

The solution to expand-2(1+a^{1/2}x+ay)^2 is -4a^{1/2}x-2ax^2-4a^{3/2}xy-4ay-2a^2y^2-2

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expand-2(1+a^{1/2}x+ay)^2

expand

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

- 4 a^{\frac{1}{2}} x - 2 a x^{2} - 4 a^{\frac{3}{2}} x y - 4 a y - 2 a^{2} y^{2} - 2

Solution steps

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

(1 + a^{\frac{1}{2}} x + a y)^{2} = 2 a^{\frac{1}{2}} x + a x^{2} + 2 a^{\frac{3}{2}} x y + 2 a y + a^{2} y^{2} + 1

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

Distribute parentheses

= (- 2) \cdot 2 a^{\frac{1}{2}} x + (- 2) a x^{2} + (- 2) \cdot 2 a^{\frac{3}{2}} x y + (- 2) \cdot 2 a y + (- 2) a^{2} y^{2} + (- 2) \cdot 1

Apply minus-plus rules

+ (- a) = - a

= - 2 \cdot 2 a^{\frac{1}{2}} x - 2 a x^{2} - 2 \cdot 2 a^{\frac{3}{2}} x y - 2 \cdot 2 a y - 2 a^{2} y^{2} - 2 \cdot 1

Simplify

- 2 \cdot 2 a^{\frac{1}{2}} x - 2 a x^{2} - 2 \cdot 2 a^{\frac{3}{2}} x y - 2 \cdot 2 a y - 2 a^{2} y^{2} - 2 \cdot 1 : - 4 a^{\frac{1}{2}} x - 2 a x^{2} - 4 a^{\frac{3}{2}} x y - 4 a y - 2 a^{2} y^{2} - 2

= - 4 a^{\frac{1}{2}} x - 2 a x^{2} - 4 a^{\frac{3}{2}} x y - 4 a y - 2 a^{2} y^{2} - 2

\frac{5 ( 3 x - 2 )}{3 x - 6}

\frac{( 2 x + c ) ^{3}}{8}

sin (3 (t - \frac{π}{2}))

\frac{5}{3} + \frac{7}{4}

csc (s) (arctan (6) + π)

What is expand-2(1+a^{1/2}x+ay)^2 ?
The solution to expand-2(1+a^{1/2}x+ay)^2 is -4a^{1/2}x-2ax^2-4a^{3/2}xy-4ay-2a^2y^2-2