What is expand (2x+1)^6 ?

The solution to expand (2x+1)^6 is 64x^6+192x^5+240x^4+160x^3+60x^2+12x+1

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expand (2x+1)^6

expand

(2 x + 1)^{6}

64 x^{6} + 192 x^{5} + 240 x^{4} + 160 x^{3} + 60 x^{2} + 12 x + 1

Solution steps

(2 x + 1)^{6}

Apply binomial theorem:

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

a = 2 x, b = 1

= i = 0 \sum 6 (i 6) (2 x)^{(6 - i)} \cdot 1^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (2 x)^{6} \cdot 1^{0} : 64 x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (2 x)^{5} \cdot 1^{1} : 192 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (2 x)^{4} \cdot 1^{2} : 240 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (2 x)^{3} \cdot 1^{3} : 160 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (2 x)^{2} \cdot 1^{4} : 60 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (2 x)^{1} \cdot 1^{5} : 12 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (2 x)^{0} \cdot 1^{6} : 1

= 64 x^{6} + 192 x^{5} + 240 x^{4} + 160 x^{3} + 60 x^{2} + 12 x + 1

\frac{cos ^{2} ( θ )}{cot ^{2} ( θ )}

\frac{1}{1 + 7}

(a^{2} \cdot a^{- 5})^{- 3} \cdot (a \cdot a^{3})^{4}

\frac{x ^{11}}{x ^{4}}

100 - 60 e^{- 0.2 \cdot 12}

What is expand (2x+1)^6 ?
The solution to expand (2x+1)^6 is 64x^6+192x^5+240x^4+160x^3+60x^2+12x+1