What is expand (3+2x)^6 ?

The solution to expand (3+2x)^6 is 729+2916x+4860x^2+4320x^3+2160x^4+576x^5+64x^6

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expand (3+2x)^6

expand

(3 + 2 x)^{6}

729 + 2916 x + 4860 x^{2} + 4320 x^{3} + 2160 x^{4} + 576 x^{5} + 64 x^{6}

Solution steps

(3 + 2 x)^{6}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 3, b = 2 x

= i = 0 \sum 6 (i 6) \cdot 3^{(6 - i)} (2 x)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 3^{6} (2 x)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 3^{5} (2 x)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 3^{4} (2 x)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 3^{3} (2 x)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 3^{2} (2 x)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 3^{1} (2 x)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 3^{0} (2 x)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 3^{6} (2 x)^{0} : 729

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 3^{5} (2 x)^{1} : 2916 x

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 3^{4} (2 x)^{2} : 4860 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 3^{3} (2 x)^{3} : 4320 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 3^{2} (2 x)^{4} : 2160 x^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 3^{1} (2 x)^{5} : 576 x^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 3^{0} (2 x)^{6} : 64 x^{6}

= 729 + 2916 x + 4860 x^{2} + 4320 x^{3} + 2160 x^{4} + 576 x^{5} + 64 x^{6}

m^{3} - 8

\frac{27}{8}

(2 t - 3)^{3}

2 (x^{2} - 4) - 2 (6 x^{2} + 2)

\frac{x}{3} + \frac{x}{7}

What is expand (3+2x)^6 ?
The solution to expand (3+2x)^6 is 729+2916x+4860x^2+4320x^3+2160x^4+576x^5+64x^6