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Popular >

expand (1-x/4)^{10}

Solution

expand

(1 - \frac{x}{4})^{10}

Solution

1 - \frac{5 x}{2} + \frac{45 x ^{2}}{16} - \frac{15 x ^{3}}{8} + \frac{105 x ^{4}}{128} - \frac{63 x ^{5}}{256} + \frac{105 x ^{6}}{2048} - \frac{15 x ^{7}}{2048} + \frac{45 x ^{8}}{65536} - \frac{5 x ^{9}}{131072} + \frac{x ^{10}}{1048576}

Solution steps

(1 - \frac{x}{4})^{10}

Apply binomial theorem:

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

a = 1, b = - \frac{x}{4}

= i = 0 \sum 10 (i 10) \cdot 1^{(10 - i)} (- \frac{x}{4})^{i}

Expand summation

= \frac{10 !}{0 ! ( 10 - 0 ) !} \cdot 1^{10} (- \frac{x}{4})^{0} + \frac{10 !}{1 ! ( 10 - 1 ) !} \cdot 1^{9} (- \frac{x}{4})^{1} + \frac{10 !}{2 ! ( 10 - 2 ) !} \cdot 1^{8} (- \frac{x}{4})^{2} + \frac{10 !}{3 ! ( 10 - 3 ) !} \cdot 1^{7} (- \frac{x}{4})^{3} + \frac{10 !}{4 ! ( 10 - 4 ) !} \cdot 1^{6} (- \frac{x}{4})^{4} + \frac{10 !}{5 ! ( 10 - 5 ) !} \cdot 1^{5} (- \frac{x}{4})^{5} + \frac{10 !}{6 ! ( 10 - 6 ) !} \cdot 1^{4} (- \frac{x}{4})^{6} + \frac{10 !}{7 ! ( 10 - 7 ) !} \cdot 1^{3} (- \frac{x}{4})^{7} + \frac{10 !}{8 ! ( 10 - 8 ) !} \cdot 1^{2} (- \frac{x}{4})^{8} + \frac{10 !}{9 ! ( 10 - 9 ) !} \cdot 1^{1} (- \frac{x}{4})^{9} + \frac{10 !}{10 ! ( 10 - 10 ) !} \cdot 1^{0} (- \frac{x}{4})^{10}

Simplify

\frac{10 !}{0 ! ( 10 - 0 ) !} \cdot 1^{10} (- \frac{x}{4})^{0} : 1

Simplify

\frac{10 !}{1 ! ( 10 - 1 ) !} \cdot 1^{9} (- \frac{x}{4})^{1} : - \frac{5 x}{2}

Simplify

\frac{10 !}{2 ! ( 10 - 2 ) !} \cdot 1^{8} (- \frac{x}{4})^{2} : \frac{45 x ^{2}}{16}

Simplify

\frac{10 !}{3 ! ( 10 - 3 ) !} \cdot 1^{7} (- \frac{x}{4})^{3} : - \frac{15 x ^{3}}{8}

Simplify

\frac{10 !}{4 ! ( 10 - 4 ) !} \cdot 1^{6} (- \frac{x}{4})^{4} : \frac{105 x ^{4}}{128}

Simplify

\frac{10 !}{5 ! ( 10 - 5 ) !} \cdot 1^{5} (- \frac{x}{4})^{5} : - \frac{63 x ^{5}}{256}

Simplify

\frac{10 !}{6 ! ( 10 - 6 ) !} \cdot 1^{4} (- \frac{x}{4})^{6} : \frac{105 x ^{6}}{2048}

Simplify

\frac{10 !}{7 ! ( 10 - 7 ) !} \cdot 1^{3} (- \frac{x}{4})^{7} : - \frac{15 x ^{7}}{2048}

Simplify

\frac{10 !}{8 ! ( 10 - 8 ) !} \cdot 1^{2} (- \frac{x}{4})^{8} : \frac{45 x ^{8}}{65536}

Simplify

\frac{10 !}{9 ! ( 10 - 9 ) !} \cdot 1^{1} (- \frac{x}{4})^{9} : - \frac{5 x ^{9}}{131072}

Simplify

\frac{10 !}{10 ! ( 10 - 10 ) !} \cdot 1^{0} (- \frac{x}{4})^{10} : \frac{x ^{10}}{1048576}

= 1 - \frac{5 x}{2} + \frac{45 x ^{2}}{16} - \frac{15 x ^{3}}{8} + \frac{105 x ^{4}}{128} - \frac{63 x ^{5}}{256} + \frac{105 x ^{6}}{2048} - \frac{15 x ^{7}}{2048} + \frac{45 x ^{8}}{65536} - \frac{5 x ^{9}}{131072} + \frac{x ^{10}}{1048576}

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Frequently Asked Questions (FAQ)

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