What is expand (x-1)^2sin(1/(x-1)) ?

The solution to expand (x-1)^2sin(1/(x-1)) is sin(1/(x-1))x^2-2xsin(1/(x-1))+sin(1/(x-1))

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expand (x-1)^2sin(1/(x-1))

expand

(x - 1)^{2} sin (\frac{1}{x - 1})

sin (\frac{1}{x - 1}) x^{2} - 2 x sin (\frac{1}{x - 1}) + sin (\frac{1}{x - 1})

Solution steps

(x - 1)^{2} sin (\frac{1}{x - 1})

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

Expand

(x - 1)^{2} : x^{2} - 2 x + 1

= sin (\frac{1}{x - 1}) (x^{2} - 2 x + 1)

Apply the distributive law:

m (a + b + c) = ma + mb + m c

sin (\frac{1}{x - 1}) (x^{2} - 2 x + 1) = sin (\frac{1}{x - 1}) x^{2} + sin (\frac{1}{x - 1}) (- 2 x) + sin (\frac{1}{x - 1}) \cdot 1

= sin (\frac{1}{x - 1}) x^{2} + sin (\frac{1}{x - 1}) (- 2 x) + sin (\frac{1}{x - 1}) \cdot 1

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

sin (\frac{1}{x - 1}) \cdot 1 = sin (\frac{1}{x - 1})

= sin (\frac{1}{x - 1}) x^{2} - 2 x sin (\frac{1}{x - 1}) + sin (\frac{1}{x - 1})

\frac{( e ^{x} + e ^{- x} ) ^{2}}{4}

\frac{8 x - 5}{( 4 x - 7 ) ^{2}}

x^{2} (10 - \frac{x ^{2}}{2})

(\frac{4}{2 - 5 x})^{3}

\frac{7 ( x + h ) ^{2}}{2}

What is expand (x-1)^2sin(1/(x-1)) ?
The solution to expand (x-1)^2sin(1/(x-1)) is sin(1/(x-1))x^2-2xsin(1/(x-1))+sin(1/(x-1))