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

The solution to expand (2/3 b+3/4)^3 is (1728b^2+512b^3+1944b+729)/(1728)

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expand (2/3 b+3/4)^3

expand

(\frac{2}{3} b + \frac{3}{4})^{3}

\frac{1728 b ^{2} + 512 b ^{3} + 1944 b + 729}{1728}

Solution steps

(\frac{2}{3} b + \frac{3}{4})^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

(\frac{2}{3} b)^{3} + 3 (\frac{2}{3} b)^{2} \frac{3}{4} + 3 \cdot \frac{2}{3} b (\frac{3}{4})^{2} + (\frac{3}{4})^{3} : \frac{1728 b ^{2} + 512 b ^{3} + 1944 b + 729}{1728}

= \frac{1728 b ^{2} + 512 b ^{3} + 1944 b + 729}{1728}

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What is expand (2/3 b+3/4)^3 ?
The solution to expand (2/3 b+3/4)^3 is (1728b^2+512b^3+1944b+729)/(1728)