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Popular >

expand (n+1)^5

Solution

expand

(n + 1)^{5}

Solution

n^{5} + 5 n^{4} + 10 n^{3} + 10 n^{2} + 5 n + 1

Solution steps

(n + 1)^{5}

Apply binomial theorem:

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

a = n, b = 1

= i = 0 \sum 5 (i 5) n^{(5 - i)} \cdot 1^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} n^{5} \cdot 1^{0} : n^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} n^{4} \cdot 1^{1} : 5 n^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} n^{3} \cdot 1^{2} : 10 n^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} n^{2} \cdot 1^{3} : 10 n^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} n^{1} \cdot 1^{4} : 5 n

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} n^{0} \cdot 1^{5} : 1

= n^{5} + 5 n^{4} + 10 n^{3} + 10 n^{2} + 5 n + 1

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Frequently Asked Questions (FAQ)

What is expand (n+1)^5 ?
The solution to expand (n+1)^5 is n^5+5n^4+10n^3+10n^2+5n+1