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

The solution to expand (x/3+4)^3 is (x^3+36x^2+432x+1728)/(27)

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expand (x/3+4)^3

expand

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

\frac{x ^{3} + 36 x ^{2} + 432 x + 1728}{27}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(\frac{x}{3})^{3} + 3 (\frac{x}{3})^{2} \cdot 4 + 3 \cdot \frac{x}{3} \cdot 4^{2} + 4^{3} : \frac{x ^{3} + 36 x ^{2} + 432 x + 1728}{27}

= \frac{x ^{3} + 36 x ^{2} + 432 x + 1728}{27}

\frac{6}{4} + \frac{3}{3} + \frac{8}{6}

3 \times (- 7)

3 \times 2 x

7 \times 7 \times 7

What is expand (x/3+4)^3 ?
The solution to expand (x/3+4)^3 is (x^3+36x^2+432x+1728)/(27)