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

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

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expand (3x+2)^6

expand

(3 x + 2)^{6}

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

Solution steps

(3 x + 2)^{6}

Apply binomial theorem:

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

a = 3 x, b = 2

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(m + n + 1) (m + n - 1)

4 i (6 i)

2 x^{3} - x^{3}

a a

\frac{sec ( x ) - cos ( x )}{sec ( x )}

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