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

The solution to (1/2*x+1/3*y)^3 is (x^3)/8+(x^2y)/4+(xy^2)/6+(y^3)/(27)

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

simplify

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

\frac{x ^{3}}{8} + \frac{x ^{2} y}{4} + \frac{x y ^{2}}{6} + \frac{y ^{3}}{27}

Solution steps

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

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

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

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

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

(\frac{x}{2})^{3} + 3 (\frac{x}{2})^{2} \frac{y}{3} + 3 \cdot \frac{x}{2} (\frac{y}{3})^{2} + (\frac{y}{3})^{3} : \frac{x ^{3}}{8} + \frac{x ^{2} y}{4} + \frac{x y ^{2}}{6} + \frac{y ^{3}}{27}

= \frac{x ^{3}}{8} + \frac{x ^{2} y}{4} + \frac{x y ^{2}}{6} + \frac{y ^{3}}{27}

3 (b - 4 c)^{2} - a (b - 4 c)^{3}

lo g_{10} (\frac{( x ^{2} + 2 )}{( x ^{2} )})

(- 6 a^{2})^{3}

(y - z) p + (2 - x) q - x - y

(2 a^{- 3} \cdot b^{2})^{3}

What is (1/2*x+1/3*y)^3 ?
The solution to (1/2*x+1/3*y)^3 is (x^3)/8+(x^2y)/4+(xy^2)/6+(y^3)/(27)