化简 (x-2)(x+2)(x+3)-(x+1)^3

解答

化简

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

- 7 x - 13

求解步骤

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

展开

(x - 2) (x + 2) (x + 3) : x^{3} + 3 x^{2} - 4 x - 12

= x^{3} + 3 x^{2} - 4 x - 12 - (x + 1)^{3}

展开

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

= x^{3} + 3 x^{2} - 4 x - 12 - x^{3} - 3 x^{2} - 3 x - 1

对同类项分组

= x^{3} - x^{3} + 3 x^{2} - 3 x^{2} - 4 x - 3 x - 12 - 1

s im pl i f y 15 (x - 3 y) - 3 \cdot (3 x - x)^{2}

s im pl i f y (- 3 a^{3})^{4}

e x p an d (25 - x)^{3}

e x p an d (m - 3)^{4}

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