What is expand (2+x)^6 ?

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

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expand (2+x)^6

expand

(2 + x)^{6}

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

Solution steps

(2 + x)^{6}

Apply binomial theorem:

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

a = 2, b = x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(2 s + 6 i - 4 m) + (7 s - 2 i - 2 m)

- 0.75 - 0.4

(7 + 3 i)^{2}

\frac{( \frac{x}{2} - 1 )}{x - 2}

2 a^{2} - 5 a - 12

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