展开 (1+x)sqrt(3)(2x-1)

解答

展开

(1 + x) 3 (2 x - 1)

23 x^{2} + 3 x - 3

求解步骤

(1 + x) 3 (2 x - 1)

= 3 (1 + x) (2 x - 1)

Apply FOIL method

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

= 3 (2 x^{2} + x - 1)

使用分配律:

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

3 (2 x^{2} + x - 1) = 3 \cdot 2 x^{2} + 3 x + 3 (- 1)

= 3 \cdot 2 x^{2} + 3 x + 3 (- 1)

化简

3 \cdot 2 x^{2} + 3 x + 3 (- 1) : 23 x^{2} + 3 x - 3

= 23 x^{2} + 3 x - 3

e x p an d 2 (5 + 6)

s im pl i f y (x - 3) (x + 1) (x - \frac{1}{2}) (x - 5)

e x p an d (6 x^{6} - x^{2} y) + (- x^{3} + x^{2} y^{2}) y^{'} (x)

e x p an d e^{5 x} (5 x e^{5 x} + e^{5 x})

e x p an d (sin (x) + c)^{2}