What is expand (x-7)(x-6)^8ln(x/5) ?

The solution to expand (x-7)(x-6)^8ln(x/5) is

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expand (x-7)(x-6)^8ln(x/5)

expand

(x - 7) (x - 6)^{8} ln (\frac{x}{5})

x^{9} ln (\frac{x}{5}) - 55 x^{8} ln (\frac{x}{5}) + 1344 x^{7} ln (\frac{x}{5}) - 19152 x^{6} ln (\frac{x}{5}) + 175392 x^{5} ln (\frac{x}{5}) - 1070496 x^{4} ln (\frac{x}{5}) + 4354560 x^{3} ln (\frac{x}{5}) - 11384064 x^{2} ln (\frac{x}{5}) + 17356032 x ln (\frac{x}{5}) - 11757312 ln (\frac{x}{5})

Solution steps

(x - 7) (x - 6)^{8} ln (\frac{x}{5})

= ln (\frac{x}{5}) (x - 7) (x - 6)^{8}

Apply the distributive law:

a (b - c) = ab - a c

a = (x - 6)^{8} ln (\frac{x}{5}), b = x, c = 7

= (x - 6)^{8} ln (\frac{x}{5}) x - (x - 6)^{8} ln (\frac{x}{5}) \cdot 7

= x ln (\frac{x}{5}) (x - 6)^{8} - 7 ln (\frac{x}{5}) (x - 6)^{8}

Simplify

x ln (\frac{x}{5}) (x - 6)^{8} - 7 ln (\frac{x}{5}) (x - 6)^{8} : x^{9} ln (\frac{x}{5}) - 55 x^{8} ln (\frac{x}{5}) + 1344 x^{7} ln (\frac{x}{5}) - 19152 x^{6} ln (\frac{x}{5}) + 175392 x^{5} ln (\frac{x}{5}) - 1070496 x^{4} ln (\frac{x}{5}) + 4354560 x^{3} ln (\frac{x}{5}) - 11384064 x^{2} ln (\frac{x}{5}) + 17356032 x ln (\frac{x}{5}) - 11757312 ln (\frac{x}{5})

= x^{9} ln (\frac{x}{5}) - 55 x^{8} ln (\frac{x}{5}) + 1344 x^{7} ln (\frac{x}{5}) - 19152 x^{6} ln (\frac{x}{5}) + 175392 x^{5} ln (\frac{x}{5}) - 1070496 x^{4} ln (\frac{x}{5}) + 4354560 x^{3} ln (\frac{x}{5}) - 11384064 x^{2} ln (\frac{x}{5}) + 17356032 x ln (\frac{x}{5}) - 11757312 ln (\frac{x}{5})

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

(x - 4)^{3}

(ln (x)) (- x^{3} + 3)

(1 - e^{- c})^{2}

t^{2} cos (ln (t)) \cdot (2 t sin (ln (t)) + t cos (ln (t)))

What is expand (x-7)(x-6)^8ln(x/5) ?
The solution to expand (x-7)(x-6)^8ln(x/5) is