Effectuer, réduire. Factoriser.

Effectuer, r´eduire. Factoriser.
Faire disparaˆıtre les parenth`eses et r´eduire :
1. a2−(b2−c2)+b2−(a2+c2)−c2−(a2−b2)
2. (4a3−2a2+a+1)−(−a2+3a3−a−7) −(a3−4a2+8+2a)
3. (2a−3b+4c)−(5c−5a−4b)+(b+c−7a)
4. 6a+3b−(5a+2b+3c)+(−4a−3b)
5. (6a+5b)−(4a+b−3c)−(2c+5a+3b)
6. 3a2b2+4b4−(a3b−4a2b2−3ab3+2b4)−ab3−(4a2b2+3b4)+3a4
7. a2−(b2−c2)−[b2−(c2−a2)] −[c2−(b2−a2)]
8. [a3+b3−(3a2b+3ab2)] −[(a3−3a2b)−(3ab2−b3)]
9. (a+2b−6a)−[3b−(6a−6b)] −[(a−3b)−(2a+5b)]
10. 7x−[−3x−[4x−(5x−2y)] −(−3y+2x)]
11. 2x−(3y+3z)−[5y−(6z−6y)+5z−[4x−(2z−5y)]]
Effectuer et r´eduire :
1. 91x2y2z2−7x2y(13yz2−9y2z)−21y3z(3x2−2z2)
2. 9x2yz(2xy2z2−4x5y6z6)−3x3y5z7(x8y6z4−13x4y2)
3. 13x2b2(8x5b7−2x4b9)−2x4b5(9x3b4−13x2b6)
4. (x+y−z)z+(x−y+z)y+(−x+y+z)x−2[x(y−x)+y(z−y)+z(x−z)]
5. [a2+(n−1)a+1]a+[a2−(n−1)a+1]a
6. a[2a+b−(a+2b)] + a[3a−2b−(2a−3b)] −a[a+3b−(2a+2b)]
7. 15a2+24b2−(3a+2b)(5a+6b)
8. 2ab +a(9a+8b)−(8a−9b)(5a+7b)−(3a−2b)(5a+8b)
9. (3a−6b)(4a−3b)−[(2a−5b)(6a−11b)−(37b2−6ab)]
10. (3a3−2a2+a−1)(5a2−4a−1) −(15a4−12a3+3a2−a−1)(a−1)

11. (a2−b2)(2a3−4a2b−5ab2)−(b2−a2)(4a3+8a2b+5ab2)
12. [(x−y)a2−(x−y)a+(x−y)][(x+y)a2+(x+y)a+(x+y)]
13. (x2−y2)(2x−3y+5z)+(y−x)(3x2+4yz −5xz)+(y2−x2)(4x−3y+z)
Factoriser les expressions suivantes :
1. xy +y
2. mx +xp
3. x3a2−x2a3
4. 4xz −2xy
5. 6x2y+4xy
6. 24y3z5−36yz2
7. 3x3y4−12x2y3
8. 15x7y2−10x5y3
9. 3x2yz2−xyz3
10. b(y−x)−a(y−x)
11. x(a2+b2)−y(a2+b2)
12. 2yz5−6y2z4+6y3z3−2y4z2
13. 2x3y2+8x3y3−6x4y
14. 3a3b2c−9a2b3c2+18a4b2c2
15. x(y−z)−y(y−z)+z(y−z)
16. 10xz2+15x2z
17. 12a2b2−18ab3+24a3b
18. 12x2a3−30x3a2+18xa4
19. x(a+b)+y(a+b)
20. (x−y)+a(x−y)

Solutions
1. a2−(b2−c2)+b2−(a2+c2)−c2−(a2−b2)=−a2+b2−c2
2. (4a3−2a2+a+1)−(−a2+3a3−a−7) −(a3−4a2+8+2a)=3a2
3. (2a−3b+4c)−(5c−5a−4b)+(b+c−7a)=2b
4. 6a+3b−(5a+2b+3c)+(−4a−3b)=−3a−2b−3c
5. (6a+5b)−(4a+b−3c)−(2c+5a+3b)=−3a+b+c
6. 3a2b2+4b4−(a3b−4a2b2−3ab3+2b4)−ab3−(4a2b2+3b4)+3a4
=3a2b2−b4−a3b+2ab3+3a4
7. a2−(b2−c2)−[b2−(c2−a2)] −[c2−(b2−a2)] = a2−b2+c2
8. [a3+b3−(3a2b+3ab2)] −[(a3−3a2b)−(3ab2−b3)] = 0
9. (a+2b−6a)−[3b−(6a−6b)] −[(a−3b)−(2a+5b)] = 2a+b
10. 7x−[−3x−[4x−(5x−2y)] −(−3y+2x)] = 11x−y
11. 2x−(3y+3z)−[5y−(6z−6y)+5z−[4x−(2z−5y)]] = 6x−9y−4z
Effectuer et r´eduire :
1. 91x2y2z2−7x2y(13yz2−9y2z)−21y3z(3x2−2z2)=42y3z3
2. 9x2yz(2xy2z2−4x5y6z6)−3x3y5z7(x8y6z4−13x4y2)=18x3y3z3+3x7y7z7−3x11y11z11
3. 13x2b2(8x5b7−2x4b9)−2x4b5(9x3b4−13x2b6)=86x7b9
4. (x+y−z)z+(x−y+z)y+(−x+y+z)x−2[x(y−x)+y(z−y)+z(x−z)] = z2+y2+x2
5. [a2+(n−1)a+1]a+[a2−(n−1)a+1]a=2a3+2a
6. a[2a+b−(a+2b)] + a[3a−2b−(2a−3b)] −a[a+3b−(2a+2b)] = 3a2−ab
7. 15a2+24b2−(3a+2b)(5a+6b)=12b2−28ab
8. 2ab +a(9a+8b)−(8a−9b)(5a+7b)−(3a−2b)(5a+8b)=−15ab −46a2+79b2
9. (3a−6b)(4a−3b)−[(2a−5b)(6a−11b)−(37b2−6ab)] = 13ab
10. (3a3−2a2+a−1)(5a2−4a−1)−(15a4−12a3+3a2−a−1)(a−1) = 5a4−5a3−3a2+3a
11. (a2−b2)(2a3−4a2b−5ab2)−(b2−a2)(4a3+8a2b+5ab2)=6a5+4a4b−6a3b2−4b3a2

12. [(x−y)a2−(x−y)a+(x−y)][(x+y)a2+(x+y)a+(x+y)]
=x2−y2+x2a4+x2a2−a4y2−a2y2
13. (x2−y2)(2x−3y+5z)+(y−x)(3x2+4yz −5xz)+(y2−x2)(4x−3y+z)
=−5x3+3x2y+9x2z+2y2x−9xyz
Factoriser les expressions suivantes :
1. xy +y=y(x+1)
2. mx +xp =x(m+p)
3. x3a2−x2a3=a2x2(x−a)
4. 4xz −2xy =2x(2z−y)
5. 6x2y+4xy =2xy (3x+2)
6. 24y3z5−36yz2=12yz2(2z3y2−3)
7. 3x3y4−12x2y3=3x2y3(xy −4)
8. 15x7y2−10x5y3=5x5y2(3x2−2y)
9. 3x2yz2−xyz3=xyz2(−z+3x)
10. b(y−x)−a(y−x)=(x−y)(a−b)
11. x(a2+b2)−y(a2+b2)=(a2+b2)(x−y)
12. 2yz5−6y2z4+6y3z3−2y4z2=2yz2(z3−3yz2+3y2z−y3)
13. 2x3y2+8x3y3−6x4y=2x3y(4y2+y−3x)
14. 3a3b2c−9a2b3c2+18a4b2c2=3a2b2c(−3bc +6ca2+a)
15. x(y−z)−y(y−z)+z(y−z)=(y−z)(x−y+z)
16. 10xz2+15x2z=5xz (2z+3x)
17. 12a2b2−18ab3+24a3b=6ab (2ab −3b2+4a2)
18. 12x2a3−30x3a2+18xa4=6xa2(3a+5x)(−x+a)
19. x(a+b)+y(a+b)=(x+y)(a+b)
20. (x−y)+a(x−y)=(x−y)(a+1)