What is expand 2((sqrt(3))/2 x-1/2 y)^2 ?

The solution to expand 2((sqrt(3))/2 x-1/2 y)^2 is (3x^2+y^2-2sqrt(3)xy)/2

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expand 2((sqrt(3))/2 x-1/2 y)^2

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(\frac{3}{2} x)^{2} - 2 \cdot \frac{3}{2} x \frac{1}{2} y + (\frac{1}{2} y)^{2} : \frac{3 x ^{2} + y ^{2} - 2 3 x y}{4}

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

Simplify

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

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

\frac{7}{s ( s + 3 ) ( s + 2 )}

\frac{x ^{2} - 4 x + 3}{( x + 1 ) ^{2}}

\frac{1}{s ( s + a ) ^{2}}

(\frac{3 i}{n})^{3}

(e + \frac{1}{e})^{2}

What is expand 2((sqrt(3))/2 x-1/2 y)^2 ?
The solution to expand 2((sqrt(3))/2 x-1/2 y)^2 is (3x^2+y^2-2sqrt(3)xy)/2