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

The solution to expand (1/2 x+(sqrt(3))/2 y)^2 is (x^2+3y^2+2xsqrt(3)y)/4

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

23 (- 0.4 e^{- 0.4 x} + 5.6 e^{- 5.6 x})

(1 - i 3)^{10}

\frac{y ^{3} + 2 y ^{2} - 1}{y}

3 \cdot ((5, 10, 7) + (2, - 3, 7))

e^{2 jk w} (e^{4 jk w} + e^{- 4 jk w})

What is expand (1/2 x+(sqrt(3))/2 y)^2 ?
The solution to expand (1/2 x+(sqrt(3))/2 y)^2 is (x^2+3y^2+2xsqrt(3)y)/4