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

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

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

simplify

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

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

Solution steps

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

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

\frac{1}{3} y = \frac{y}{3}

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(- 2 x + 2) 2 - 3 (2 x - 2) (x + 3)

- 2 x + 11 + x - 1 + (- 2) x + 11 + x - 1

\frac{1}{( 2 - \frac{2}{a} )} + \frac{1}{( \frac{2}{a} - 2 )}

(x^{5} + y^{5}) (x^{10} - x^{5} y^{5} + y^{10})

a^{4} b^{2} + a^{2} b^{4}

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