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

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

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expand (2x+3)^6

expand

(2 x + 3)^{6}

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

Solution steps

(2 x + 3)^{6}

Apply binomial theorem:

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

a = 2 x, b = 3

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

x^{2} - 23 + 120

13 - (2 + 7 i) + 5 i

\frac{x ^{3} + 8}{x ^{2} - 2 x + 4}

(5 - 6) (5 + 6)

\frac{- 5 - 9 i}{9 + 8 i}

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