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Popular >

expand (x-2/3)^8

Solution

expand

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

Solution

x^{8} - \frac{16 x ^{7}}{3} + \frac{112 x ^{6}}{9} - \frac{448 x ^{5}}{27} + \frac{1120 x ^{4}}{81} - \frac{1792 x ^{3}}{243} + \frac{1792 x ^{2}}{729} - \frac{1024 x}{2187} + \frac{256}{6561}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} (- \frac{2}{3})^{1} : - \frac{16 x ^{7}}{3}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} (- \frac{2}{3})^{2} : \frac{112 x ^{6}}{9}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} (- \frac{2}{3})^{3} : - \frac{448 x ^{5}}{27}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} (- \frac{2}{3})^{4} : \frac{1120 x ^{4}}{81}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} (- \frac{2}{3})^{5} : - \frac{1792 x ^{3}}{243}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} (- \frac{2}{3})^{6} : \frac{1792 x ^{2}}{729}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} (- \frac{2}{3})^{7} : - \frac{1024 x}{2187}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} (- \frac{2}{3})^{8} : \frac{256}{6561}

= x^{8} - \frac{16 x ^{7}}{3} + \frac{112 x ^{6}}{9} - \frac{448 x ^{5}}{27} + \frac{1120 x ^{4}}{81} - \frac{1792 x ^{3}}{243} + \frac{1792 x ^{2}}{729} - \frac{1024 x}{2187} + \frac{256}{6561}

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