What is expand (4+x)^6 ?

The solution to expand (4+x)^6 is 4096+6144x+3840x^2+1280x^3+240x^4+24x^5+x^6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (4+x)^6

expand

(4 + x)^{6}

4096 + 6144 x + 3840 x^{2} + 1280 x^{3} + 240 x^{4} + 24 x^{5} + x^{6}

Solution steps

(4 + x)^{6}

Apply binomial theorem:

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

a = 4, b = x

= i = 0 \sum 6 (i 6) \cdot 4^{(6 - i)} x^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 4^{6} x^{0} : 4096

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 4^{5} x^{1} : 6144 x

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 4^{4} x^{2} : 3840 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 4^{3} x^{3} : 1280 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 4^{2} x^{4} : 240 x^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 4^{1} x^{5} : 24 x^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 4^{0} x^{6} : x^{6}

= 4096 + 6144 x + 3840 x^{2} + 1280 x^{3} + 240 x^{4} + 24 x^{5} + x^{6}

\frac{3}{5} + \frac{4}{15}

\frac{x ^{4}}{x ^{- 3}}

(x + 4) (x - 4) - (x + 8) (x - 2)

\frac{7}{12} \div 2

What is expand (4+x)^6 ?
The solution to expand (4+x)^6 is 4096+6144x+3840x^2+1280x^3+240x^4+24x^5+x^6