What is expand (x+2)^9 ?

The solution to expand (x+2)^9 is x^9+18x^8+144x^7+672x^6+2016x^5+4032x^4+5376x^3+4608x^2+2304x+512

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expand (x+2)^9

expand

(x + 2)^{9}

x^{9} + 18 x^{8} + 144 x^{7} + 672 x^{6} + 2016 x^{5} + 4032 x^{4} + 5376 x^{3} + 4608 x^{2} + 2304 x + 512

Solution steps

(x + 2)^{9}

Apply binomial theorem:

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

a = x, b = 2

= i = 0 \sum 9 (i 9) x^{(9 - i)} \cdot 2^{i}

Expand summation

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

Simplify

\frac{9 !}{0 ! ( 9 - 0 ) !} x^{9} \cdot 2^{0} : x^{9}

Simplify

\frac{9 !}{1 ! ( 9 - 1 ) !} x^{8} \cdot 2^{1} : 18 x^{8}

Simplify

\frac{9 !}{2 ! ( 9 - 2 ) !} x^{7} \cdot 2^{2} : 144 x^{7}

Simplify

\frac{9 !}{3 ! ( 9 - 3 ) !} x^{6} \cdot 2^{3} : 672 x^{6}

Simplify

\frac{9 !}{4 ! ( 9 - 4 ) !} x^{5} \cdot 2^{4} : 2016 x^{5}

Simplify

\frac{9 !}{5 ! ( 9 - 5 ) !} x^{4} \cdot 2^{5} : 4032 x^{4}

Simplify

\frac{9 !}{6 ! ( 9 - 6 ) !} x^{3} \cdot 2^{6} : 5376 x^{3}

Simplify

\frac{9 !}{7 ! ( 9 - 7 ) !} x^{2} \cdot 2^{7} : 4608 x^{2}

Simplify

\frac{9 !}{8 ! ( 9 - 8 ) !} x^{1} \cdot 2^{8} : 2304 x

Simplify

\frac{9 !}{9 ! ( 9 - 9 ) !} x^{0} \cdot 2^{9} : 512

= x^{9} + 18 x^{8} + 144 x^{7} + 672 x^{6} + 2016 x^{5} + 4032 x^{4} + 5376 x^{3} + 4608 x^{2} + 2304 x + 512

f (x) - g (x)

2 x (3 x - 2 y) - 9 x y + 6 y^{2}

\frac{1 + 3}{2}

545 - 80

\frac{a x - 3 b x + a y - 3 b y}{a ^{2} - 9 b ^{2}}

What is expand (x+2)^9 ?
The solution to expand (x+2)^9 is x^9+18x^8+144x^7+672x^6+2016x^5+4032x^4+5376x^3+4608x^2+2304x+512