What is expand (p+q)^5 ?

The solution to expand (p+q)^5 is p^5+5p^4q+10p^3q^2+10p^2q^3+5pq^4+q^5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (p+q)^5

expand

(p + q)^{5}

p^{5} + 5 p^{4} q + 10 p^{3} q^{2} + 10 p^{2} q^{3} + 5 p q^{4} + q^{5}

Solution steps

(p + q)^{5}

Apply binomial theorem:

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

a = p, b = q

= i = 0 \sum 5 (i 5) p^{(5 - i)} q^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} p^{5} q^{0} : p^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} p^{4} q^{1} : 5 p^{4} q

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} p^{3} q^{2} : 10 p^{3} q^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} p^{2} q^{3} : 10 p^{2} q^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} p^{1} q^{4} : 5 p q^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} p^{0} q^{5} : q^{5}

= p^{5} + 5 p^{4} q + 10 p^{3} q^{2} + 10 p^{2} q^{3} + 5 p q^{4} + q^{5}

(p + q)^{3}

4 a - 1 - 4 ab + b

5 ln ((e^{\frac{7 x}{5}})^{5})

\frac{π}{4} \div 2

What is expand (p+q)^5 ?
The solution to expand (p+q)^5 is p^5+5p^4q+10p^3q^2+10p^2q^3+5pq^4+q^5