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

The solution to expand (2x+2/3 x^3)^3 is (216x^3+216x^5+72x^7+8x^9)/(27)

Popular >

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

expand

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

\frac{216 x ^{3} + 216 x ^{5} + 72 x ^{7} + 8 x ^{9}}{27}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(2 x)^{3} + 3 (2 x)^{2} \frac{2}{3} x^{3} + 3 \cdot 2 x (\frac{2}{3} x^{3})^{2} + (\frac{2}{3} x^{3})^{3} : \frac{216 x ^{3} + 216 x ^{5} + 72 x ^{7} + 8 x ^{9}}{27}

= \frac{216 x ^{3} + 216 x ^{5} + 72 x ^{7} + 8 x ^{9}}{27}

- \frac{x ( - 2 x + 12 )}{9}

r sin (θ) (e^{r^{2} c o s (θ)} + r sin (θ))

(e^{t} + e^{- t})^{2}

\frac{2 ( - 3 x ^{2} + 7 )}{( 3 x ^{2} + 7 ) ^{2}}

\frac{8}{( e ^{2 x} + e ^{- 2 x} ) ^{2}}

What is expand (2x+2/3 x^3)^3 ?
The solution to expand (2x+2/3 x^3)^3 is (216x^3+216x^5+72x^7+8x^9)/(27)