mathematica练习程序（第二章 初等代数运算）

习题：

代码如下：

1.
Expand[(x + 1) (x^2 - 2 x + 3)]

Expand[(3 a - 2) (a - 1) + (a + 1) (a + 2)]

Expand[x (y - z) + y (z - x) + z (x - y)]

Expand[(2 x^2 - 1) (x - 4) - (x^2 + 3) (2 x - 5)]

2.
x = -4;
(x - 2) (x^2 + 2 x + 4) + (x + 5) (x^2 - 5 x + 25)

y = 1/2;
(y - 2) (y^2 - 6 y - 9) - y (y^2 - 2 y - 15)

3.
Clear[x]
Factor[x^5 - x^3]

Factor[x^4 - y^4]

Factor[16 - x^4]

Factor[x^3 - 6 x^2 + 11 x - 6]

Factor[(x + y)^2 - 10 (x + y) + 25]

Factor[x^2/3 + xy + y^2]

Factor[3 a x + 4 b y + 4 a y + 3 b x]

Factor[x^4 + 4 x^3 - 19 x^2 - 46 x + 120]

4.
Factor[(x^2 + y^2 - z^2 + 2 x y)/(x^2 - y^2 + z^2 - 2 x z)]

Factor[(a x^3 - a y^3)/(x^2 - y^2)]

5.
Factor[(x^2 + 2 x + 4)/(x^2 + 4 x + 
      4) / ((x^3 - 8)/(3 x + 6)) / (1/(x^2 - 4))]

Factor[1/(x + 1) - (x + 
     3) (x^2 - 2 x + 1)/((x^2 - 1) (x^2 + 4 x + 3))]

Factor[a/((a - b) (a - c)) + b/((b - c) (b - a)) + 
  c/((c - a) (c - b))]

N[(2 Sqrt[2] + 3 Sqrt[3])/(3 Sqrt[2] - 2 Sqrt[3])]

6.
Clear[y]
Solve[(y - 3)^2 - (y + 3)^3 == 9 y (1 - 2 y), y]

Solve[3 x^2 + 5 (2 x + 1) == 0, x]

Solve[a b x^2 + (a^4 + b^4) x + a^3 b^3 == 0, x]

Solve[x^2 - (2 m + 1) x + m^2 + m == 0, x]

Solve[{4 x^2 - 9 y^2 == 15, 2 x - 3 y == 15}, {x, y}]

Solve[{x^2 + 2 x y + y^2 == 9, (x - y^2 - 3 (x - y) - 10 == 0)}, {x, 
  y}]

Solve[{Sqrt[3] x + Sqrt[3] y == Sqrt[7], 
  Sqrt[6] x - Sqrt[7] == Sqrt[5]}, {x, y}]