展开 (3x-2)(xln(x)-x)

解答

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(3 x - 2) (x ln (x) - x)

3 x^{2} ln (x) - 3 x^{2} - 2 x ln (x) + 2 x

求解步骤

(3 x - 2) (x ln (x) - x)

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = 3 x, b = - 2, c = x ln (x), d = - x

= 3 xx ln (x) + 3 x (- x) + (- 2) x ln (x) + (- 2) (- x)

使用加减运算法则

+ (- a) = - a, (- a) (- b) = ab

= 3 xx ln (x) - 3 xx - 2 x ln (x) + 2 x

化简

3 xx ln (x) - 3 xx - 2 x ln (x) + 2 x : 3 x^{2} ln (x) - 3 x^{2} - 2 x ln (x) + 2 x

= 3 x^{2} ln (x) - 3 x^{2} - 2 x ln (x) + 2 x

e x p an d \frac{( 80 - t ) ^{2}}{2}

e x p an d \frac{1}{x ^{4} ( s + 1 )}

e x p an d (\frac{4}{x + 3}) (\frac{1}{2 - x})

e x p an d (5 x^{2} - 4 + 7) - (3 x^{2} = 7 x - 1)

e x p an d 20 (e^{- 2 t} sin (t) - e^{- 2 t} \cdot t \cdot cos (t))