What is expand (3-x/2-3/2 y)^2 ?

The solution to expand (3-x/2-3/2 y)^2 is 9-3x-9y+(x^2)/4+(3xy)/2+(9y^2)/4

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expand (3-x/2-3/2 y)^2

expand

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

9 - 3 x - 9 y + \frac{x ^{2}}{4} + \frac{3 x y}{2} + \frac{9 y ^{2}}{4}

Solution steps

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

Multiply

\frac{3}{2} y : \frac{3 y}{2}

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

Combine the fractions

- \frac{x}{2} - \frac{3 y}{2} : \frac{- x - 3 y}{2}

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

Apply Perfect Square Formula:

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

a = 3, b = \frac{- x - 3 y}{2}

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

Simplify

3^{2} + 2 \cdot 3 \cdot \frac{- x - 3 y}{2} + (\frac{- x - 3 y}{2})^{2} : 9 - 3 x - 9 y + \frac{x ^{2} + 6 x y + 9 y ^{2}}{4}

= 9 - 3 x - 9 y + \frac{x ^{2} + 6 x y + 9 y ^{2}}{4}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{2} + 6 x y + 9 y ^{2}}{4} = \frac{x ^{2}}{4} + \frac{6 x y}{4} + \frac{9 y ^{2}}{4}

= 9 - 3 x - 9 y + \frac{x ^{2}}{4} + \frac{6 x y}{4} + \frac{9 y ^{2}}{4}

Cancel

\frac{6 x y}{4} : \frac{3 x y}{2}

= 9 - 3 x - 9 y + \frac{x ^{2}}{4} + \frac{3 x y}{2} + \frac{9 y ^{2}}{4}

6 (\frac{2}{3} - 2 y)

2 cos (x) (3 - 7 tan (x))

(2 a - a b)^{4}

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

(a + b \cdot i)^{3}

What is expand (3-x/2-3/2 y)^2 ?
The solution to expand (3-x/2-3/2 y)^2 is 9-3x-9y+(x^2)/4+(3xy)/2+(9y^2)/4