What is expand (a+2/3 bx)^3 ?

The solution to expand (a+2/3 bx)^3 is (27a^3+54bxa^2+36ab^2x^2+8b^3x^3)/(27)

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expand (a+2/3 bx)^3

expand

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

\frac{27 a ^{3} + 54 b x a ^{2} + 36 a b ^{2} x ^{2} + 8 b ^{3} x ^{3}}{27}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

a^{3} + 3 a^{2} \frac{2}{3} b x + 3 a (\frac{2}{3} b x)^{2} + (\frac{2}{3} b x)^{3} : \frac{27 a ^{3} + 54 b x a ^{2} + 36 a b ^{2} x ^{2} + 8 b ^{3} x ^{3}}{27}

= \frac{27 a ^{3} + 54 b x a ^{2} + 36 a b ^{2} x ^{2} + 8 b ^{3} x ^{3}}{27}

\frac{( x - 2 ) ^{2}}{4}

(1 + sin (x))^{(2)} + (ln (x))^{(2 x)}

3 \cdot 5 \cdot (2 \cdot 2 - 7)

2 (1 + cos (θ))^{2}

- \frac{1}{( x + 1 ) ^{2} ( x + 6 )}

What is expand (a+2/3 bx)^3 ?
The solution to expand (a+2/3 bx)^3 is (27a^3+54bxa^2+36ab^2x^2+8b^3x^3)/(27)