What is expand (yz+1)^5 ?

The solution to expand (yz+1)^5 is y^5z^5+5y^4z^4+10y^3z^3+10y^2z^2+5yz+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (yz+1)^5

expand

(yz + 1)^{5}

y^{5} z^{5} + 5 y^{4} z^{4} + 10 y^{3} z^{3} + 10 y^{2} z^{2} + 5 yz + 1

Solution steps

(yz + 1)^{5}

Apply binomial theorem:

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

a = yz, b = 1

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (yz)^{5} \cdot 1^{0} : y^{5} z^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (yz)^{4} \cdot 1^{1} : 5 y^{4} z^{4}

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= y^{5} z^{5} + 5 y^{4} z^{4} + 10 y^{3} z^{3} + 10 y^{2} z^{2} + 5 yz + 1

\frac{5 x}{x ^{2}}

(n + 2)^{2}

(- 10 - 3 i)^{2}

\frac{18}{27}

9 a^{2}

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