What is expand (1+2/3 x)^n(3+nx)^2 ?

The solution to expand (1+2/3 x)^n(3+nx)^2 is (1+2/3 x)^n*9+(1+2/3 x)^n*6nx+(1+2/3 x)^nn^2x^2

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expand (1+2/3 x)^n(3+nx)^2

expand

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

(1 + \frac{2}{3} x)^{n} \cdot 9 + (1 + \frac{2}{3} x)^{n} \cdot 6 n x + (1 + \frac{2}{3} x)^{n} n^{2} x^{2}

Solution steps

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

Expand

(3 + n x)^{2} : 9 + 6 n x + n^{2} x^{2}

= (1 + \frac{2}{3} x)^{n} (9 + 6 n x + n^{2} x^{2})

Apply the distributive law:

m (a + b + c) = ma + mb + m c

(1 + \frac{2}{3} x)^{n} (9 + 6 n x + n^{2} x^{2}) = (1 + \frac{2}{3} x)^{n} \cdot 9 + (1 + \frac{2}{3} x)^{n} \cdot 6 n x + (1 + \frac{2}{3} x)^{n} n^{2} x^{2}

= (1 + \frac{2}{3} x)^{n} \cdot 9 + (1 + \frac{2}{3} x)^{n} \cdot 6 n x + (1 + \frac{2}{3} x)^{n} n^{2} x^{2}

(x + 1) \times (x - \frac{1}{6})

((x^{2} - 13 x) \cdot (x + 3)) x

(x - 67) (x + 67)

\frac{4 ( x - 4 ) e ^{8 x}}{( x - 8 ) ^{3}}

x^{2 (n + 1)}

What is expand (1+2/3 x)^n(3+nx)^2 ?
The solution to expand (1+2/3 x)^n(3+nx)^2 is (1+2/3 x)^n*9+(1+2/3 x)^n*6nx+(1+2/3 x)^nn^2x^2