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Popular >

expand (3/5 x-y/2)^8

Solution

expand

(\frac{3}{5} x - \frac{y}{2})^{8}

Solution

\frac{1679616 x ^{8} + 390625 y ^{8}}{100000000} - \frac{8748 x ^{7} y}{78125} + \frac{5103 x ^{6} y ^{2}}{15625} - \frac{1701 x ^{5} y ^{3}}{3125} + \frac{567 x ^{4} y ^{4}}{1000} - \frac{189 x ^{3} y ^{5}}{500} + \frac{63 x ^{2} y ^{6}}{400} - \frac{3 x y ^{7}}{80}

Solution steps

(\frac{3}{5} x - \frac{y}{2})^{8}

Apply binomial theorem:

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

a = \frac{3}{5} x, b = - \frac{y}{2}

= i = 0 \sum 8 (i 8) (\frac{3}{5} x)^{(8 - i)} (- \frac{y}{2})^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} (\frac{3}{5} x)^{8} (- \frac{y}{2})^{0} : \frac{6561 x ^{8}}{390625}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} (\frac{3}{5} x)^{7} (- \frac{y}{2})^{1} : - \frac{8748 x ^{7} y}{78125}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} (\frac{3}{5} x)^{6} (- \frac{y}{2})^{2} : \frac{5103 x ^{6} y ^{2}}{15625}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} (\frac{3}{5} x)^{5} (- \frac{y}{2})^{3} : - \frac{1701 x ^{5} y ^{3}}{3125}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} (\frac{3}{5} x)^{4} (- \frac{y}{2})^{4} : \frac{567 x ^{4} y ^{4}}{1000}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} (\frac{3}{5} x)^{3} (- \frac{y}{2})^{5} : - \frac{189 x ^{3} y ^{5}}{500}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} (\frac{3}{5} x)^{2} (- \frac{y}{2})^{6} : \frac{63 x ^{2} y ^{6}}{400}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} (\frac{3}{5} x)^{1} (- \frac{y}{2})^{7} : - \frac{3 x y ^{7}}{80}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} (\frac{3}{5} x)^{0} (- \frac{y}{2})^{8} : \frac{y ^{8}}{256}

= \frac{6561 x ^{8}}{390625} - \frac{8748 x ^{7} y}{78125} + \frac{5103 x ^{6} y ^{2}}{15625} - \frac{1701 x ^{5} y ^{3}}{3125} + \frac{567 x ^{4} y ^{4}}{1000} - \frac{189 x ^{3} y ^{5}}{500} + \frac{63 x ^{2} y ^{6}}{400} - \frac{3 x y ^{7}}{80} + \frac{y ^{8}}{256}

Simplify

\frac{6561 x ^{8}}{390625} - \frac{8748 x ^{7} y}{78125} + \frac{5103 x ^{6} y ^{2}}{15625} - \frac{1701 x ^{5} y ^{3}}{3125} + \frac{567 x ^{4} y ^{4}}{1000} - \frac{189 x ^{3} y ^{5}}{500} + \frac{63 x ^{2} y ^{6}}{400} - \frac{3 x y ^{7}}{80} + \frac{y ^{8}}{256} : \frac{1679616 x ^{8} + 390625 y ^{8}}{100000000} - \frac{8748 x ^{7} y}{78125} + \frac{5103 x ^{6} y ^{2}}{15625} - \frac{1701 x ^{5} y ^{3}}{3125} + \frac{567 x ^{4} y ^{4}}{1000} - \frac{189 x ^{3} y ^{5}}{500} + \frac{63 x ^{2} y ^{6}}{400} - \frac{3 x y ^{7}}{80}

= \frac{1679616 x ^{8} + 390625 y ^{8}}{100000000} - \frac{8748 x ^{7} y}{78125} + \frac{5103 x ^{6} y ^{2}}{15625} - \frac{1701 x ^{5} y ^{3}}{3125} + \frac{567 x ^{4} y ^{4}}{1000} - \frac{189 x ^{3} y ^{5}}{500} + \frac{63 x ^{2} y ^{6}}{400} - \frac{3 x y ^{7}}{80}

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