What is expand (1+x)^9 ?

The solution to expand (1+x)^9 is 1+9x+36x^2+84x^3+126x^4+126x^5+84x^6+36x^7+9x^8+x^9

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expand (1+x)^9

expand

(1 + x)^{9}

1 + 9 x + 36 x^{2} + 84 x^{3} + 126 x^{4} + 126 x^{5} + 84 x^{6} + 36 x^{7} + 9 x^{8} + x^{9}

Solution steps

(1 + x)^{9}

Apply binomial theorem:

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

a = 1, b = x

= i = 0 \sum 9 (i 9) \cdot 1^{(9 - i)} x^{i}

Expand summation

= \frac{9 !}{0 ! ( 9 - 0 ) !} \cdot 1^{9} x^{0} + \frac{9 !}{1 ! ( 9 - 1 ) !} \cdot 1^{8} x^{1} + \frac{9 !}{2 ! ( 9 - 2 ) !} \cdot 1^{7} x^{2} + \frac{9 !}{3 ! ( 9 - 3 ) !} \cdot 1^{6} x^{3} + \frac{9 !}{4 ! ( 9 - 4 ) !} \cdot 1^{5} x^{4} + \frac{9 !}{5 ! ( 9 - 5 ) !} \cdot 1^{4} x^{5} + \frac{9 !}{6 ! ( 9 - 6 ) !} \cdot 1^{3} x^{6} + \frac{9 !}{7 ! ( 9 - 7 ) !} \cdot 1^{2} x^{7} + \frac{9 !}{8 ! ( 9 - 8 ) !} \cdot 1^{1} x^{8} + \frac{9 !}{9 ! ( 9 - 9 ) !} \cdot 1^{0} x^{9}

Simplify

\frac{9 !}{0 ! ( 9 - 0 ) !} \cdot 1^{9} x^{0} : 1

Simplify

\frac{9 !}{1 ! ( 9 - 1 ) !} \cdot 1^{8} x^{1} : 9 x

Simplify

\frac{9 !}{2 ! ( 9 - 2 ) !} \cdot 1^{7} x^{2} : 36 x^{2}

Simplify

\frac{9 !}{3 ! ( 9 - 3 ) !} \cdot 1^{6} x^{3} : 84 x^{3}

Simplify

\frac{9 !}{4 ! ( 9 - 4 ) !} \cdot 1^{5} x^{4} : 126 x^{4}

Simplify

\frac{9 !}{5 ! ( 9 - 5 ) !} \cdot 1^{4} x^{5} : 126 x^{5}

Simplify

\frac{9 !}{6 ! ( 9 - 6 ) !} \cdot 1^{3} x^{6} : 84 x^{6}

Simplify

\frac{9 !}{7 ! ( 9 - 7 ) !} \cdot 1^{2} x^{7} : 36 x^{7}

Simplify

\frac{9 !}{8 ! ( 9 - 8 ) !} \cdot 1^{1} x^{8} : 9 x^{8}

Simplify

\frac{9 !}{9 ! ( 9 - 9 ) !} \cdot 1^{0} x^{9} : x^{9}

= 1 + 9 x + 36 x^{2} + 84 x^{3} + 126 x^{4} + 126 x^{5} + 84 x^{6} + 36 x^{7} + 9 x^{8} + x^{9}

\frac{32}{2}

\frac{180}{6}

\frac{20}{13}

1 + \frac{1}{1 + \frac{1}{x}}

What is expand (1+x)^9 ?
The solution to expand (1+x)^9 is 1+9x+36x^2+84x^3+126x^4+126x^5+84x^6+36x^7+9x^8+x^9