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

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

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simplify (3/2 x+2/3 y)^2

simplify

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

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

Solution steps

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

Multiply

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

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

Multiply

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

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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12 x^{3} - 25 x^{2} - 38 x + 15

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