What is expand (x+6)^6 ?

The solution to expand (x+6)^6 is x^6+36x^5+540x^4+4320x^3+19440x^2+46656x+46656

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expand (x+6)^6

expand

(x + 6)^{6}

x^{6} + 36 x^{5} + 540 x^{4} + 4320 x^{3} + 19440 x^{2} + 46656 x + 46656

Solution steps

(x + 6)^{6}

Apply binomial theorem:

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

a = x, b = 6

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

Expand summation

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

Simplify

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

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} x^{5} \cdot 6^{1} : 36 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} \cdot 6^{2} : 540 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} \cdot 6^{3} : 4320 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} \cdot 6^{4} : 19440 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} \cdot 6^{5} : 46656 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} \cdot 6^{6} : 46656

= x^{6} + 36 x^{5} + 540 x^{4} + 4320 x^{3} + 19440 x^{2} + 46656 x + 46656

\frac{24}{- 2}

\frac{7 - 7}{7}

(x + 1) \cdot (x^{2} + x + 1)

(x + h) (x + h)

\frac{57}{4}

What is expand (x+6)^6 ?
The solution to expand (x+6)^6 is x^6+36x^5+540x^4+4320x^3+19440x^2+46656x+46656