What is expand 9(9/n x+1)^3 ?

The solution to expand 9(9/n x+1)^3 is (9(729x^3+27xn^2+243nx^2+n^3))/(n^3)

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expand 9(9/n x+1)^3

expand

9 (\frac{9}{n} x + 1)^{3}

\frac{9 ( 729 x ^{3} + 27 x n ^{2} + 243 n x ^{2} + n ^{3} )}{n ^{3}}

Solution steps

9 (\frac{9}{n} x + 1)^{3}

Apply Perfect Cube Formula:

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

(\frac{9}{n} x + 1)^{3} = (\frac{9}{n} x)^{3} + 3 (\frac{9}{n} x)^{2} \cdot 1 + 3 \cdot \frac{9}{n} x \cdot 1^{2} + 1^{3}

= 9 ((\frac{9}{n} x)^{3} + 3 (\frac{9}{n} x)^{2} \cdot 1 + 3 \cdot \frac{9}{n} x \cdot 1^{2} + 1^{3})

Simplify

(\frac{9}{n} x)^{3} + 3 (\frac{9}{n} x)^{2} \cdot 1 + 3 \cdot \frac{9}{n} x \cdot 1^{2} + 1^{3} : \frac{729 x ^{3} + 27 x n ^{2} + 243 n x ^{2} + n ^{3}}{n ^{3}}

= 9 \cdot \frac{729 x ^{3} + 27 x n ^{2} + 243 n x ^{2} + n ^{3}}{n ^{3}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{9 ( 729 x ^{3} + 27 x n ^{2} + 243 n x ^{2} + n ^{3} )}{n ^{3}}

sin (x) (cos (x) + 1)

2 \times (5)

\frac{( ( x + 2 ) ( x - 4 ) )}{( x + 4 ) ( x - 5 ) ( x + 1 )}

(\frac{x}{5} + \frac{3}{80}) (2 x + 1)^{\frac{3}{2}}

\frac{2 x ^{2} + 7 x - 6}{( x + 5 ) ( x - 4 )}

What is expand 9(9/n x+1)^3 ?
The solution to expand 9(9/n x+1)^3 is (9(729x^3+27xn^2+243nx^2+n^3))/(n^3)