What is expand (3/2 x+4y^2)^3 ?

The solution to expand (3/2 x+4y^2)^3 is (27x^3+216y^2x^2+576xy^4+512y^6)/8

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expand (3/2 x+4y^2)^3

expand

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

\frac{27 x ^{3} + 216 y ^{2} x ^{2} + 576 x y ^{4} + 512 y ^{6}}{8}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(\frac{3}{2} x)^{3} + 3 (\frac{3}{2} x)^{2} \cdot 4 y^{2} + 3 \cdot \frac{3}{2} x (4 y^{2})^{2} + (4 y^{2})^{3} : \frac{27 x ^{3} + 216 y ^{2} x ^{2} + 576 x y ^{4} + 512 y ^{6}}{8}

= \frac{27 x ^{3} + 216 y ^{2} x ^{2} + 576 x y ^{4} + 512 y ^{6}}{8}

((1) - sin (x)) (1 + sin (x))

(\frac{x}{4} - \frac{4}{x})^{14}

\frac{π ( 10 10 - 1 )}{27}

\frac{10 e ^{- 7 s}}{s ( s + 3 )}

(- \frac{1}{8} e^{- 4 x} + \frac{1}{12} e^{- 3 x}) (\frac{2}{3} e^{2 x})

What is expand (3/2 x+4y^2)^3 ?
The solution to expand (3/2 x+4y^2)^3 is (27x^3+216y^2x^2+576xy^4+512y^6)/8