What is expand ((x-1}{2x})(3-\frac{2x)/9)^8 ?

The solution to expand ((x-1}{2x})(3-\frac{2x)/9)^8 is

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expand ((x-1}{2x})(3-\frac{2x)/9)^8

expand

(\frac{x - 1}{2 x}) (3 - \frac{2 x}{9})^{8}

504 x^{2} - 2448 x + \frac{6561 ( x - 1 )}{2 x} - \frac{224 ( x - 1 ) x ^{2}}{3} + \frac{560 ( x - 1 ) x ^{3}}{81} - \frac{896 ( x - 1 ) x ^{4}}{2187} + \frac{896 ( x - 1 ) x ^{5}}{59049} - \frac{512 ( x - 1 ) x ^{6}}{1594323} + \frac{128 ( x - 1 ) x ^{7}}{43046721} + 1944

Solution steps

(\frac{x - 1}{2 x}) (3 - \frac{2 x}{9})^{8}

Apply rule:

(a) = a

(\frac{x - 1}{2 x}) = \frac{x - 1}{2 x}

= \frac{x - 1}{2 x} (3 - \frac{2 x}{9})^{8}

Expand

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

= \frac{x - 1}{2 x} (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})

Distribute parentheses

= \frac{x - 1}{2 x} \cdot 6561 + \frac{x - 1}{2 x} (- 3888 x) + \frac{x - 1}{2 x} \cdot 1008 x^{2} + \frac{x - 1}{2 x} (- \frac{448 x ^{3}}{3}) + \frac{x - 1}{2 x} \cdot \frac{1120 x ^{4}}{81} + \frac{x - 1}{2 x} (- \frac{1792 x ^{5}}{2187}) + \frac{x - 1}{2 x} \cdot \frac{1792 x ^{6}}{59049} + \frac{x - 1}{2 x} (- \frac{1024 x ^{7}}{1594323}) + \frac{x - 1}{2 x} \cdot \frac{256 x ^{8}}{43046721}

Simplify

\frac{x - 1}{2 x} \cdot 6561 + \frac{x - 1}{2 x} (- 3888 x) + \frac{x - 1}{2 x} \cdot 1008 x^{2} + \frac{x - 1}{2 x} (- \frac{448 x ^{3}}{3}) + \frac{x - 1}{2 x} \cdot \frac{1120 x ^{4}}{81} + \frac{x - 1}{2 x} (- \frac{1792 x ^{5}}{2187}) + \frac{x - 1}{2 x} \cdot \frac{1792 x ^{6}}{59049} + \frac{x - 1}{2 x} (- \frac{1024 x ^{7}}{1594323}) + \frac{x - 1}{2 x} \cdot \frac{256 x ^{8}}{43046721} : 504 x^{2} - 2448 x + \frac{6561 ( x - 1 )}{2 x} - \frac{224 ( x - 1 ) x ^{2}}{3} + \frac{560 ( x - 1 ) x ^{3}}{81} - \frac{896 ( x - 1 ) x ^{4}}{2187} + \frac{896 ( x - 1 ) x ^{5}}{59049} - \frac{512 ( x - 1 ) x ^{6}}{1594323} + \frac{128 ( x - 1 ) x ^{7}}{43046721} + 1944

= 504 x^{2} - 2448 x + \frac{6561 ( x - 1 )}{2 x} - \frac{224 ( x - 1 ) x ^{2}}{3} + \frac{560 ( x - 1 ) x ^{3}}{81} - \frac{896 ( x - 1 ) x ^{4}}{2187} + \frac{896 ( x - 1 ) x ^{5}}{59049} - \frac{512 ( x - 1 ) x ^{6}}{1594323} + \frac{128 ( x - 1 ) x ^{7}}{43046721} + 1944

(3 x^{2} - y)^{2}

2 \frac{3}{2}

3.14 \cdot 1^{2}

2 x^{2} y^{- 3} x^{4}

5 - 2 (\frac{36}{9 \cdot 2 - 3 ( 5 ^{0} - 2 ^{3} )}) + 16

What is expand ((x-1}{2x})(3-\frac{2x)/9)^8 ?
The solution to expand ((x-1}{2x})(3-\frac{2x)/9)^8 is