What is expand (n+1)^6 ?

The solution to expand (n+1)^6 is n^6+6n^5+15n^4+20n^3+15n^2+6n+1

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expand (n+1)^6

expand

(n + 1)^{6}

n^{6} + 6 n^{5} + 15 n^{4} + 20 n^{3} + 15 n^{2} + 6 n + 1

Solution steps

(n + 1)^{6}

Apply binomial theorem:

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

a = n, b = 1

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

Expand summation

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

Simplify

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

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} n^{5} \cdot 1^{1} : 6 n^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} n^{4} \cdot 1^{2} : 15 n^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} n^{3} \cdot 1^{3} : 20 n^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} n^{2} \cdot 1^{4} : 15 n^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} n^{1} \cdot 1^{5} : 6 n

Simplify

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

= n^{6} + 6 n^{5} + 15 n^{4} + 20 n^{3} + 15 n^{2} + 6 n + 1

13 (2 x + 5) - x

\frac{1}{4} \times 3

5 (3 x + 10)^{3}

\frac{x ^{2} - 6 x + 8}{x ^{2} - 5 x + 4}

100 - 25

What is expand (n+1)^6 ?
The solution to expand (n+1)^6 is n^6+6n^5+15n^4+20n^3+15n^2+6n+1