What is (2/3*m+3/2*n)^2 ?

The solution to (2/3*m+3/2*n)^2 is (4m^2)/9+2mn+(9n^2)/4

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simplify (2/3m+3/2n)^2

simplify

(\frac{2}{3} \cdot m + \frac{3}{2} \cdot n)^{2}

\frac{4 m ^{2}}{9} + 2 mn + \frac{9 n ^{2}}{4}

Solution steps

(\frac{2}{3} m + \frac{3}{2} n)^{2}

Multiply

\frac{2}{3} m : \frac{2 m}{3}

= (\frac{2 m}{3} + \frac{3}{2} n)^{2}

Multiply

\frac{3}{2} n : \frac{3 n}{2}

= (\frac{2 m}{3} + \frac{3 n}{2})^{2}

Apply Perfect Square Formula:

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

a = \frac{2 m}{3}, b = \frac{3 n}{2}

= (\frac{2 m}{3})^{2} + 2 \cdot \frac{2 m}{3} \cdot \frac{3 n}{2} + (\frac{3 n}{2})^{2}

Simplify

(\frac{2 m}{3})^{2} + 2 \cdot \frac{2 m}{3} \cdot \frac{3 n}{2} + (\frac{3 n}{2})^{2} : \frac{4 m ^{2}}{9} + 2 mn + \frac{9 n ^{2}}{4}

= \frac{4 m ^{2}}{9} + 2 mn + \frac{9 n ^{2}}{4}

15 x^{2} - 12 y^{2}

100 x^{2} - (x^{2} + 25)^{2}

(\frac{4 x}{5 - 2})^{3}

\frac{251}{2} \cdot \frac{84}{3}

(5 x - 3 y + 7) + (3 x + y - 3) + (4 x - y - 2)

What is (2/3*m+3/2*n)^2 ?
The solution to (2/3*m+3/2*n)^2 is (4m^2)/9+2mn+(9n^2)/4