展开 (x-8)(x-3)^6ln(x/4)

解答

展开

(x - 8) (x - 3)^{6} ln (\frac{x}{4})

x^{7} ln (\frac{x}{4}) - 26 x^{6} ln (\frac{x}{4}) + 279 x^{5} ln (\frac{x}{4}) - 1620 x^{4} ln (\frac{x}{4}) + 5535 x^{3} ln (\frac{x}{4}) - 11178 x^{2} ln (\frac{x}{4}) + 12393 x ln (\frac{x}{4}) - 5832 ln (\frac{x}{4})

求解步骤

(x - 8) (x - 3)^{6} ln (\frac{x}{4})

= ln (\frac{x}{4}) (x - 8) (x - 3)^{6}

使用分配律:

a (b - c) = ab - a c

a = (x - 3)^{6} ln (\frac{x}{4}), b = x, c = 8

= (x - 3)^{6} ln (\frac{x}{4}) x - (x - 3)^{6} ln (\frac{x}{4}) \cdot 8

= x ln (\frac{x}{4}) (x - 3)^{6} - 8 ln (\frac{x}{4}) (x - 3)^{6}

化简

x ln (\frac{x}{4}) (x - 3)^{6} - 8 ln (\frac{x}{4}) (x - 3)^{6} : x^{7} ln (\frac{x}{4}) - 26 x^{6} ln (\frac{x}{4}) + 279 x^{5} ln (\frac{x}{4}) - 1620 x^{4} ln (\frac{x}{4}) + 5535 x^{3} ln (\frac{x}{4}) - 11178 x^{2} ln (\frac{x}{4}) + 12393 x ln (\frac{x}{4}) - 5832 ln (\frac{x}{4})

= x^{7} ln (\frac{x}{4}) - 26 x^{6} ln (\frac{x}{4}) + 279 x^{5} ln (\frac{x}{4}) - 1620 x^{4} ln (\frac{x}{4}) + 5535 x^{3} ln (\frac{x}{4}) - 11178 x^{2} ln (\frac{x}{4}) + 12393 x ln (\frac{x}{4}) - 5832 ln (\frac{x}{4})

e x p an d (a + e)^{2} + (b + f)^{2} + (c + g)^{2} + (d + h)^{2}

e x p an d \frac{sec ( tan ( 2 x ) ) - 4}{( cos ( 2 x ) ) ^{2}}

e x p an d 37 (2 - 349)

e x p an d lo g_{10} (3 3 r^{2} s)

e x p an d (x^{4} - 4 x + 7) d x