Exercices de factorisation

Print["Factoriser si possible"];
ex[1] = 32  a^2 - 2  b^4;
ex[2]  =  a^2  x^2 - b^2  x^2;
ex[3]  =  4  x^2 - 16  a^2;
ex[4]  =  a^2  b^2  c^2 - m^2;
ex[5]  =  50  x^4 - 2  y^2;
ex[6]  =  256  x^2 - 64  a^4;
ex[7]  =  a^2  x^2 - 81  x^2;
ex[8]  =  x^4  y^2 - 121  y^2;
ex[9]  =  3  a^2  x - 3  a x^3;
ex[10]  =  
        150  a^6  b^2 - 24  a^2  b^2;
ex[11]  =  37  a^5 - 333  a^3  x;
ex[12]  =  x^4 - 81;
ex[13]  =  81  x^4 - 625  a^4;
ex[14]  =  32  x^4 - 2  a^4;
ex[15]  =  3  x^5 - 48  x y^8;
ex[16]  =  3  a x^4 - 3  a y^4;
ex[17]  =  x^11  y^4 - x^5  y^10;
ex[18]  =  m^3 - n^3;
ex[19]  =  6  x y^3 + 6  x;
ex[20]  =  32  x^5 + 243  y^5;
ex[21]  =  125  x^3 + 1;
ex[22]  =  192  x^6  y^6 - 2187  z^6;
ex[23]  =  a^7  b - a b^7;
ex[24]  =  x^10  y - x y^10;
ex[25]  =  
        a^(5  m) - 
          9  a^(3  m) y^(2  n);
ex[26]  =  32  x^5 - 243;
ex[27]  =  343  x^3 - 512  b^6;
ex[28]  =  64  x^6 - 1;
ex[29]  =  729  a^3 - 64;
ex[30]  = (a - b)^2 - c^2;
ex[
          31]  = (a + b)^2 - (x - y)^2;
ex[
          32]  = (5  a + 2  b)^2 - (2  b - 
                5  a)^2;
ex[
          33]  = (x + a)^2 - (3  x - 
                2  a)^2;
ex[
          34]  = (4  x - a)^2 - (4  a - 
                x)^2;
ex[
          35]  = (a + b + c)^2 - (a - 2  b - 
                c)^2;
ex[
          36]  = (x + 1)^2 - (x - 1)^2;
ex[
          37]  = (a + b)^3 - (a - b)^3;
ex[38]  = a^2 + 4  ab + b^2;
ex[39]  = 9  a^2 - 12  ab + 4  b^2;
ex[40]  = a^2 - a - 1/4;
ex[41]  = x^4 + 2  x^2 + 1;
ex[42]  = x^6 + 6  x^3 + 9;
ex[43]  = a b^2 - 2  abc + a c^2;
ex[44]  = x^2/16 - 3  x y/2 + 9  y^2;
ex[45]  = 4  x^2 + x y  +  y^2/16;
ex[46]  = 
        9  a^4  b^2 - 6  a^2  b c + c^2;
ex[47]  = 
        24  a^6  b c^3 + 54  a^4  b^3  c^3 - 
          72  a^5  b^2  c^3;
ex[48]  = 
        49  x^2  y^8 + 25  a^6  b^4 - 
          70  a^3  b^2  x y^4;
ex[49]  = 
        50  a^6  b^2  c^2 + 72  a^2  b^8  c^2;
ex[50]  = 
        4  a^7  x/3 + 8  a^4  x^5 + 12  a x^9;
ex[51]  = 
        144  x^5  y + 324  x^3  y^3 + 
          432  x^4  y^2;
ex[52]  = 
        270  x^9  y^3 + 750  x^3  y^7 - 
          900  x^6  y^5;
ex[53]  = 
        48  a^2  x^4  y + 9  y^2 + 64  a^4  x^8;
ex[54]  = 
        175  a^2  x^(2  m) + 280  a^2  x^m y^n + 
          112  a^2  y^(2  n);
ex[55]  = 
        a^3 - 6  a^2  b + 12  a b^2 - 8  b^3;
ex[56]  = x^3 + 9  x^2 + 27  x + 27;
ex[57]  = 
        250  x^6  y^9 + 150  x^4  y^7  z^2 + 30  x^2  y^5  z^4 + 
          2  y^3  z^6;
ex[58]  = 
        a^2 + b^2 + c^2 - 2  a b - 2  a c + 
          2 b c;
ex[59]  = 
        x^2 + y^2 - 2  x y + 2  x - 2  y + 1;
ex[60]  = 
        x^8 - 2  x^6 - 2  x^5 + x^4 + 2  x^3 + 
          x^2;
ex[61]  = 
        x^4 + 2  x^3 + 2  x^2 + 2  x + 1;
ex[62]  = a^2 - 2  a b + b^2 - 1;
ex[63]  = a^2 - y^2 - 2  x y - x^2;
ex[64]  = a^2 - b^2 + 2  b c - c^2;
ex[65]  = x^2 - 2  x - y^2 + 1;
ex[66]  = c y + y  +  c  + 1;
ex[67]  = 
        4  x^2 + 2  x - 9  y^2 - 3  y;
ex[68]  = c^2 + d - d^2 - c;
ex[69]  = 
        b^2  y - b^2 + a^2  y - 
          a^2;




Do[Print[i, ") ", ex[i]], {i, 69}]

Solutions

Do[Print[i, ") ", Factor[ex[i]]], {i, 69}]