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

The solution to (1/2 x+2/3 y)^2 is (x^2)/4+(2xy)/3+(4y^2)/9

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simplify (1/2 x+2/3 y)^2

simplify

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

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

Solution steps

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

\frac{1}{2} x = \frac{x}{2}

\frac{2}{3} y = \frac{2 y}{3}

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

x^{16} + x^{8} + 1

(x^{3} - 1)^{4}

p^{4} + 4 p^{2} + 16

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

\frac{1}{25} + \frac{( 25 x ^{4} )}{36} - \frac{( x ^{2} )}{3}

What is (1/2 x+2/3 y)^2 ?
The solution to (1/2 x+2/3 y)^2 is (x^2)/4+(2xy)/3+(4y^2)/9