What is expand (3x-(x^2)/3)^{13} ?

The solution to expand (3x-(x^2)/3)^{13} is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3x-(x^2)/3)^{13}

expand

(3 x - \frac{x ^{2}}{3})^{13}

1594323 x^{13} - 2302911 x^{14} + 1535274 x^{15} - 625482 x^{16} + 173745 x^{17} - 34749 x^{18} + 5148 x^{19} - 572 x^{20} + \frac{143 x ^{21}}{3} - \frac{715 x ^{22}}{243} + \frac{286 x ^{23}}{2187} - \frac{26 x ^{24}}{6561} + \frac{13 x ^{25}}{177147} - \frac{x ^{26}}{1594323}

Solution steps

(3 x - \frac{x ^{2}}{3})^{13}

Apply binomial theorem:

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

a = 3 x, b = - \frac{x ^{2}}{3}

= i = 0 \sum 13 (i 13) (3 x)^{(13 - i)} (- \frac{x ^{2}}{3})^{i}

Expand summation

= \frac{13 !}{0 ! ( 13 - 0 ) !} (3 x)^{13} (- \frac{x ^{2}}{3})^{0} + \frac{13 !}{1 ! ( 13 - 1 ) !} (3 x)^{12} (- \frac{x ^{2}}{3})^{1} + \frac{13 !}{2 ! ( 13 - 2 ) !} (3 x)^{11} (- \frac{x ^{2}}{3})^{2} + \frac{13 !}{3 ! ( 13 - 3 ) !} (3 x)^{10} (- \frac{x ^{2}}{3})^{3} + \frac{13 !}{4 ! ( 13 - 4 ) !} (3 x)^{9} (- \frac{x ^{2}}{3})^{4} + \frac{13 !}{5 ! ( 13 - 5 ) !} (3 x)^{8} (- \frac{x ^{2}}{3})^{5} + \frac{13 !}{6 ! ( 13 - 6 ) !} (3 x)^{7} (- \frac{x ^{2}}{3})^{6} + \frac{13 !}{7 ! ( 13 - 7 ) !} (3 x)^{6} (- \frac{x ^{2}}{3})^{7} + \frac{13 !}{8 ! ( 13 - 8 ) !} (3 x)^{5} (- \frac{x ^{2}}{3})^{8} + \frac{13 !}{9 ! ( 13 - 9 ) !} (3 x)^{4} (- \frac{x ^{2}}{3})^{9} + \frac{13 !}{10 ! ( 13 - 10 ) !} (3 x)^{3} (- \frac{x ^{2}}{3})^{10} + \frac{13 !}{11 ! ( 13 - 11 ) !} (3 x)^{2} (- \frac{x ^{2}}{3})^{11} + \frac{13 !}{12 ! ( 13 - 12 ) !} (3 x)^{1} (- \frac{x ^{2}}{3})^{12} + \frac{13 !}{13 ! ( 13 - 13 ) !} (3 x)^{0} (- \frac{x ^{2}}{3})^{13}

Simplify

\frac{13 !}{0 ! ( 13 - 0 ) !} (3 x)^{13} (- \frac{x ^{2}}{3})^{0} : 1594323 x^{13}

Simplify

\frac{13 !}{1 ! ( 13 - 1 ) !} (3 x)^{12} (- \frac{x ^{2}}{3})^{1} : - 2302911 x^{14}

Simplify

\frac{13 !}{2 ! ( 13 - 2 ) !} (3 x)^{11} (- \frac{x ^{2}}{3})^{2} : 1535274 x^{15}

Simplify

\frac{13 !}{3 ! ( 13 - 3 ) !} (3 x)^{10} (- \frac{x ^{2}}{3})^{3} : - 625482 x^{16}

Simplify

\frac{13 !}{4 ! ( 13 - 4 ) !} (3 x)^{9} (- \frac{x ^{2}}{3})^{4} : 173745 x^{17}

Simplify

\frac{13 !}{5 ! ( 13 - 5 ) !} (3 x)^{8} (- \frac{x ^{2}}{3})^{5} : - 34749 x^{18}

Simplify

\frac{13 !}{6 ! ( 13 - 6 ) !} (3 x)^{7} (- \frac{x ^{2}}{3})^{6} : 5148 x^{19}

Simplify

\frac{13 !}{7 ! ( 13 - 7 ) !} (3 x)^{6} (- \frac{x ^{2}}{3})^{7} : - 572 x^{20}

Simplify

\frac{13 !}{8 ! ( 13 - 8 ) !} (3 x)^{5} (- \frac{x ^{2}}{3})^{8} : \frac{143 x ^{21}}{3}

Simplify

\frac{13 !}{9 ! ( 13 - 9 ) !} (3 x)^{4} (- \frac{x ^{2}}{3})^{9} : - \frac{715 x ^{22}}{243}

Simplify

\frac{13 !}{10 ! ( 13 - 10 ) !} (3 x)^{3} (- \frac{x ^{2}}{3})^{10} : \frac{286 x ^{23}}{2187}

Simplify

\frac{13 !}{11 ! ( 13 - 11 ) !} (3 x)^{2} (- \frac{x ^{2}}{3})^{11} : - \frac{26 x ^{24}}{6561}

Simplify

\frac{13 !}{12 ! ( 13 - 12 ) !} (3 x)^{1} (- \frac{x ^{2}}{3})^{12} : \frac{13 x ^{25}}{177147}

Simplify

\frac{13 !}{13 ! ( 13 - 13 ) !} (3 x)^{0} (- \frac{x ^{2}}{3})^{13} : - \frac{x ^{26}}{1594323}

= 1594323 x^{13} - 2302911 x^{14} + 1535274 x^{15} - 625482 x^{16} + 173745 x^{17} - 34749 x^{18} + 5148 x^{19} - 572 x^{20} + \frac{143 x ^{21}}{3} - \frac{715 x ^{22}}{243} + \frac{286 x ^{23}}{2187} - \frac{26 x ^{24}}{6561} + \frac{13 x ^{25}}{177147} - \frac{x ^{26}}{1594323}

- i ((1 + i)^{n} - 1)

\frac{- 2 x ^{2} + 3}{( x ^{2} + 3 ) ^{\frac{5}{2}}}

\frac{cos ( x )}{2 ( 1 + sin ( x ) )}

(- 17 x y^{2} + cos (2 y)) d x + (K x^{2} y^{3} - 2 sin (2 y)) d y

(e^{2 x} - 5) sech (x^{2} + 7 x - 1)