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

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

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expand (2+3x)^6

expand

(2 + 3 x)^{6}

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

Solution steps

(2 + 3 x)^{6}

Apply binomial theorem:

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

a = 2, b = 3 x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

1 \frac{1}{2} + \frac{5}{6}

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

12 x^{3} - 3 x

(2 x^{2} - 3 y^{3})^{3}

\frac{5}{6 2}

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