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Popular >

expand (2-x/(16))^9

Solution

expand

(2 - \frac{x}{16})^{9}

Solution

512 - 144 x + 18 x^{2} - \frac{21 x ^{3}}{16} + \frac{63 x ^{4}}{1024} - \frac{63 x ^{5}}{32768} + \frac{21 x ^{6}}{524288} - \frac{9 x ^{7}}{16777216} + \frac{9 x ^{8}}{2 ^{31}} - \frac{x ^{9}}{1 6 ^{9}}

Solution steps

(2 - \frac{x}{16})^{9}

Apply binomial theorem:

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

a = 2, b = - \frac{x}{16}

= i = 0 \sum 9 (i 9) \cdot 2^{(9 - i)} (- \frac{x}{16})^{i}

Expand summation

= \frac{9 !}{0 ! ( 9 - 0 ) !} \cdot 2^{9} (- \frac{x}{16})^{0} + \frac{9 !}{1 ! ( 9 - 1 ) !} \cdot 2^{8} (- \frac{x}{16})^{1} + \frac{9 !}{2 ! ( 9 - 2 ) !} \cdot 2^{7} (- \frac{x}{16})^{2} + \frac{9 !}{3 ! ( 9 - 3 ) !} \cdot 2^{6} (- \frac{x}{16})^{3} + \frac{9 !}{4 ! ( 9 - 4 ) !} \cdot 2^{5} (- \frac{x}{16})^{4} + \frac{9 !}{5 ! ( 9 - 5 ) !} \cdot 2^{4} (- \frac{x}{16})^{5} + \frac{9 !}{6 ! ( 9 - 6 ) !} \cdot 2^{3} (- \frac{x}{16})^{6} + \frac{9 !}{7 ! ( 9 - 7 ) !} \cdot 2^{2} (- \frac{x}{16})^{7} + \frac{9 !}{8 ! ( 9 - 8 ) !} \cdot 2^{1} (- \frac{x}{16})^{8} + \frac{9 !}{9 ! ( 9 - 9 ) !} \cdot 2^{0} (- \frac{x}{16})^{9}

Simplify

\frac{9 !}{0 ! ( 9 - 0 ) !} \cdot 2^{9} (- \frac{x}{16})^{0} : 512

Simplify

\frac{9 !}{1 ! ( 9 - 1 ) !} \cdot 2^{8} (- \frac{x}{16})^{1} : - 144 x

Simplify

\frac{9 !}{2 ! ( 9 - 2 ) !} \cdot 2^{7} (- \frac{x}{16})^{2} : 18 x^{2}

Simplify

\frac{9 !}{3 ! ( 9 - 3 ) !} \cdot 2^{6} (- \frac{x}{16})^{3} : - \frac{21 x ^{3}}{16}

Simplify

\frac{9 !}{4 ! ( 9 - 4 ) !} \cdot 2^{5} (- \frac{x}{16})^{4} : \frac{63 x ^{4}}{1024}

Simplify

\frac{9 !}{5 ! ( 9 - 5 ) !} \cdot 2^{4} (- \frac{x}{16})^{5} : - \frac{63 x ^{5}}{32768}

Simplify

\frac{9 !}{6 ! ( 9 - 6 ) !} \cdot 2^{3} (- \frac{x}{16})^{6} : \frac{21 x ^{6}}{524288}

Simplify

\frac{9 !}{7 ! ( 9 - 7 ) !} \cdot 2^{2} (- \frac{x}{16})^{7} : - \frac{9 x ^{7}}{16777216}

Simplify

\frac{9 !}{8 ! ( 9 - 8 ) !} \cdot 2^{1} (- \frac{x}{16})^{8} : \frac{9 x ^{8}}{2 ^{31}}

Simplify

\frac{9 !}{9 ! ( 9 - 9 ) !} \cdot 2^{0} (- \frac{x}{16})^{9} : - \frac{x ^{9}}{1 6 ^{9}}

= 512 - 144 x + 18 x^{2} - \frac{21 x ^{3}}{16} + \frac{63 x ^{4}}{1024} - \frac{63 x ^{5}}{32768} + \frac{21 x ^{6}}{524288} - \frac{9 x ^{7}}{16777216} + \frac{9 x ^{8}}{2 ^{31}} - \frac{x ^{9}}{1 6 ^{9}}

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Frequently Asked Questions (FAQ)

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