What is (3/4 x^2y-1/3 xz)^2 ?

The solution to (3/4 x^2y-1/3 xz)^2 is (9x^4y^2}{16}-\frac{x^3yz)/2+(x^2z^2)/9

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simplify (3/4 x^2y-1/3 xz)^2

simplify

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

\frac{9 x ^{4} y ^{2}}{16} - \frac{x ^{3} yz}{2} + \frac{x ^{2} z ^{2}}{9}

Solution steps

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

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

\frac{1}{3} x z = \frac{x z}{3}

= (\frac{3 x ^{2} y}{4} - \frac{x z}{3})^{2}

Apply Perfect Square Formula:

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

a = \frac{3 x ^{2} y}{4}, b = \frac{x z}{3}

= (\frac{3 x ^{2} y}{4})^{2} - 2 \cdot \frac{3 x ^{2} y}{4} \cdot \frac{x z}{3} + (\frac{x z}{3})^{2}

Simplify

(\frac{3 x ^{2} y}{4})^{2} - 2 \cdot \frac{3 x ^{2} y}{4} \cdot \frac{x z}{3} + (\frac{x z}{3})^{2} : \frac{9 x ^{4} y ^{2}}{16} - \frac{x ^{3} yz}{2} + \frac{x ^{2} z ^{2}}{9}

= \frac{9 x ^{4} y ^{2}}{16} - \frac{x ^{3} yz}{2} + \frac{x ^{2} z ^{2}}{9}

\frac{3}{4} \cdot \frac{2}{4}

2 0^{\circ} - 2 0^{g} + \frac{3}{8} π

(3 + 5 i) + (4 + i) + (12 + 5 i)

\frac{1}{x} - \frac{1}{2 x}

(1 + a)^{2}

What is (3/4 x^2y-1/3 xz)^2 ?
The solution to (3/4 x^2y-1/3 xz)^2 is (9x^4y^2}{16}-\frac{x^3yz)/2+(x^2z^2)/9