What is expand (x-8)(4-x)^6ln(x/7) ?

The solution to expand (x-8)(4-x)^6ln(x/7) is

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expand (x-8)(4-x)^6ln(x/7)

expand

(x - 8) (4 - x)^{6} ln (\frac{x}{7})

x^{7} ln (\frac{x}{7}) - 32 x^{6} ln (\frac{x}{7}) + 432 x^{5} ln (\frac{x}{7}) - 3200 x^{4} ln (\frac{x}{7}) + 14080 x^{3} ln (\frac{x}{7}) - 36864 x^{2} ln (\frac{x}{7}) + 53248 x ln (\frac{x}{7}) - 32768 ln (\frac{x}{7})

Solution steps

(x - 8) (4 - x)^{6} ln (\frac{x}{7})

= ln (\frac{x}{7}) (x - 8) (4 - x)^{6}

Apply the distributive law:

a (b - c) = ab - a c

a = (4 - x)^{6} ln (\frac{x}{7}), b = x, c = 8

= (4 - x)^{6} ln (\frac{x}{7}) x - (4 - x)^{6} ln (\frac{x}{7}) \cdot 8

= x ln (\frac{x}{7}) (4 - x)^{6} - 8 ln (\frac{x}{7}) (4 - x)^{6}

Simplify

x ln (\frac{x}{7}) (4 - x)^{6} - 8 ln (\frac{x}{7}) (4 - x)^{6} : x^{7} ln (\frac{x}{7}) - 32 x^{6} ln (\frac{x}{7}) + 432 x^{5} ln (\frac{x}{7}) - 3200 x^{4} ln (\frac{x}{7}) + 14080 x^{3} ln (\frac{x}{7}) - 36864 x^{2} ln (\frac{x}{7}) + 53248 x ln (\frac{x}{7}) - 32768 ln (\frac{x}{7})

= x^{7} ln (\frac{x}{7}) - 32 x^{6} ln (\frac{x}{7}) + 432 x^{5} ln (\frac{x}{7}) - 3200 x^{4} ln (\frac{x}{7}) + 14080 x^{3} ln (\frac{x}{7}) - 36864 x^{2} ln (\frac{x}{7}) + 53248 x ln (\frac{x}{7}) - 32768 ln (\frac{x}{7})

(7 x^{9} + 5 x^{5} + 85 x) l e f t (x^{4} - 4)

8 δ (x - 4 π) + 2 H (x) - 2 H (x - 14)

(2 - x - 2)^{2}

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

(1 + x) e^{(1 - x)}

What is expand (x-8)(4-x)^6ln(x/7) ?
The solution to expand (x-8)(4-x)^6ln(x/7) is