What is expand (x+1)^9 ?

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

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expand (x+1)^9

expand

(x + 1)^{9}

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

Solution steps

(x + 1)^{9}

Apply binomial theorem:

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

a = x, b = 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

7 z - 3 + z \cdot 6^{2}

(2 c^{2} + d^{2})^{3}

(1 + i) (x + i y)

\frac{7}{8} + \frac{1}{16}

\frac{4}{4 - 3}

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