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Popular >

expand (3-(2x)/9)^8

Solution

expand

(3 - \frac{2 x}{9})^{8}

Solution

6561 - 3888 x + 1008 x^{2} - \frac{448 x ^{3}}{3} + \frac{1120 x ^{4}}{81} - \frac{1792 x ^{5}}{2187} + \frac{1792 x ^{6}}{59049} - \frac{1024 x ^{7}}{1594323} + \frac{256 x ^{8}}{43046721}

Solution steps

(3 - \frac{2 x}{9})^{8}

Apply binomial theorem:

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

a = 3, b = - \frac{2 x}{9}

= i = 0 \sum 8 (i 8) \cdot 3^{(8 - i)} (- \frac{2 x}{9})^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 3^{8} (- \frac{2 x}{9})^{0} : 6561

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 3^{7} (- \frac{2 x}{9})^{1} : - 3888 x

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 3^{6} (- \frac{2 x}{9})^{2} : 1008 x^{2}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 3^{5} (- \frac{2 x}{9})^{3} : - \frac{448 x ^{3}}{3}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 3^{4} (- \frac{2 x}{9})^{4} : \frac{1120 x ^{4}}{81}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 3^{3} (- \frac{2 x}{9})^{5} : - \frac{1792 x ^{5}}{2187}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 3^{2} (- \frac{2 x}{9})^{6} : \frac{1792 x ^{6}}{59049}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 3^{1} (- \frac{2 x}{9})^{7} : - \frac{1024 x ^{7}}{1594323}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 3^{0} (- \frac{2 x}{9})^{8} : \frac{256 x ^{8}}{43046721}

= 6561 - 3888 x + 1008 x^{2} - \frac{448 x ^{3}}{3} + \frac{1120 x ^{4}}{81} - \frac{1792 x ^{5}}{2187} + \frac{1792 x ^{6}}{59049} - \frac{1024 x ^{7}}{1594323} + \frac{256 x ^{8}}{43046721}

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Frequently Asked Questions (FAQ)

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