What is expand (x+6)^5 ?

The solution to expand (x+6)^5 is x^5+30x^4+360x^3+2160x^2+6480x+7776

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x+6)^5

expand

(x + 6)^{5}

x^{5} + 30 x^{4} + 360 x^{3} + 2160 x^{2} + 6480 x + 7776

Solution steps

(x + 6)^{5}

Apply binomial theorem:

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

a = x, b = 6

= i = 0 \sum 5 (i 5) x^{(5 - i)} \cdot 6^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} \cdot 6^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} \cdot 6^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} \cdot 6^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} \cdot 6^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} \cdot 6^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} \cdot 6^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} \cdot 6^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} \cdot 6^{1} : 30 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} \cdot 6^{2} : 360 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} \cdot 6^{3} : 2160 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} \cdot 6^{4} : 6480 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} \cdot 6^{5} : 7776

= x^{5} + 30 x^{4} + 360 x^{3} + 2160 x^{2} + 6480 x + 7776

9 x^{3} y^{2} + 24 x^{4} y^{3}

\frac{4 14}{12}

(2 x - 3) (5 x + 6)

\frac{x ^{2} - 1}{x - 1}

6 + 106

What is expand (x+6)^5 ?
The solution to expand (x+6)^5 is x^5+30x^4+360x^3+2160x^2+6480x+7776