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

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

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

simplify

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

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

Solution steps

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

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

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

= (\frac{x ^{2}}{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}}{2}, b = \frac{y}{3}

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

Simplify

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

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

512 x^{3} - 64 y^{3}

f (x) 3 x + 2

f (x) 3 x + 1

\frac{0}{3.14285715} + 9 - (- 2) \cdot x^{15}

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

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