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Popular >

expand (k+1)^5

Solution

expand

(k + 1)^{5}

Solution

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

Solution steps

(k + 1)^{5}

Apply binomial theorem:

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

a = k, b = 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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