en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (s+1)^5

Solution

expand

(s + 1)^{5}

Solution

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

Solution steps

(s + 1)^{5}

Apply binomial theorem:

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

a = s, b = 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

Popular Examples

factor 4x-14x^3 factor

4 x - 14 x^{3}

factor 125m^3-1331n^3 factor

125 m^{3} - 1331 n^{3}

simplify 30h^{28759}-0-0 simplify

30 h^{28759} - 0 - 0

factor 2x^3+x^2-80x-175 factor

2 x^{3} + x^{2} - 80 x - 175

simplify ((2x^4+8x^3+7x^2+4x+3))/((x+3))simplify

\frac{( 2 x ^{4} + 8 x ^{3} + 7 x ^{2} + 4 x + 3 )}{( x + 3 )}

Frequently Asked Questions (FAQ)

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