What is expand (3x+4)^6 ?

The solution to expand (3x+4)^6 is 729x^6+5832x^5+19440x^4+34560x^3+34560x^2+18432x+4096

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expand (3x+4)^6

expand

(3 x + 4)^{6}

729 x^{6} + 5832 x^{5} + 19440 x^{4} + 34560 x^{3} + 34560 x^{2} + 18432 x + 4096

Solution steps

(3 x + 4)^{6}

Apply binomial theorem:

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

a = 3 x, b = 4

= i = 0 \sum 6 (i 6) (3 x)^{(6 - i)} \cdot 4^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (3 x)^{6} \cdot 4^{0} : 729 x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (3 x)^{5} \cdot 4^{1} : 5832 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (3 x)^{4} \cdot 4^{2} : 19440 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (3 x)^{3} \cdot 4^{3} : 34560 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (3 x)^{2} \cdot 4^{4} : 34560 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (3 x)^{1} \cdot 4^{5} : 18432 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (3 x)^{0} \cdot 4^{6} : 4096

= 729 x^{6} + 5832 x^{5} + 19440 x^{4} + 34560 x^{3} + 34560 x^{2} + 18432 x + 4096

3 11 a^{7} b

a^{4} b^{2} c^{4} - 16

\frac{3 x - 1}{5} + \frac{x + 2}{5}

1 + 4 (2 - 3 k)

14 a^{2} + 15 ab + 4 b^{2}

What is expand (3x+4)^6 ?
The solution to expand (3x+4)^6 is 729x^6+5832x^5+19440x^4+34560x^3+34560x^2+18432x+4096