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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(\frac{1}{3} x)^{2} + 2 \cdot \frac{1}{3} x \frac{2}{3} y + (\frac{2}{3} y)^{2} : \frac{x ^{2} + 4 x y + 4 y ^{2}}{9}

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

(\frac{2}{3} x^{6} + \frac{1}{4} y) (\frac{2}{3} x^{6} - \frac{1}{4} y)

3 l e f t (c - 6 b + 6 z)

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

(\frac{1}{2} a + \frac{2}{3} a^{\frac{4}{5}})^{12}

(cot (θ) + csc (θ))^{2}

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