What is expand (x+4)^6 ?

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

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expand (x+4)^6

expand

(x + 4)^{6}

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

Solution steps

(x + 4)^{6}

Apply binomial theorem:

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

a = x, b = 4

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{72}{15}

\frac{( \frac{1}{5} ) ^{2}}{( \frac{1}{2} ) ^{3} + \frac{5}{3}}

ln (x^{2} (x + 2))

\frac{2}{2 - 3}

\frac{1}{- \frac{23}{6} + 8}

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