Factorización

* Factor común.

1. 2a + 4 = 2(a + 2)
2. 3b + 6 = 3(b + 2)
3. a + a2 = a(1 + a)
4. b2 + b3 = b2(1 + b)
5. 3a+4a2+5a3=a3+4a+5a2
6. 5x3+2x-3x2= 5x3-3x2+2x=x(5x2-3x+2)
7.2a3-4a+6a2= 2a3+6a2-4a=2a(a2+3a-2)
8. 4b-12b2+8b3= 8b3-12b2+4b=4b(2b2-3b+1)
9. 5m2+10m3-15m5= -15m5+10m3+5m2=5m2(-3m3+2m+1)
10. 2a3b+4a5c-6a2d= 4a5c+2a3b-6a2d= 2a2(2a3c+ab-3d)
11.8x2y-12xy2=4xy2x-3y
12. 20x3y2+25x2y3=5x2y2(4x+5y)
13. 3x2yz3+6xy2z2=3xyz2(xz+2y)
14. 14a2b2c-21ab3c2=7ab2c(2a-3bc)
15. 10a4b5x3+35a2b7x2=5a2b5x2(2a2x+7b2)
16.45ax3by+9a2xb3y=9axby(5x2+ab2)
17. 12ab+3abc+6bcd=3b(4a+ac+2cd)
18. 15ab2-25a3b+30a3b2c=5ab(3b-5a2+6a2bc)
19. 45a5b3x6y2+15a2b3x3yd=5a2b3x3y(9a3x3y+3d)
20. 35a2bc5y2-21a2bc3y+49ab2c3y3m=7abc3y(5ac2y-3a+7by2m)* Binomio como factor común.

1. x(m + n) + y(m + n) = (x + y)(m + n)
2. a(x − y) + b(x − y) = (a + b)(x - y)
3. r(m + n) − s(m + n) = (r - s)(m + n)
4. x(a + b)+ a + b = (a + b)(x + 1)
5. x(a + b) − a – b = (a + b)(x - 1)
6. a(c − d) + xc – xd = a(c - d) + x(c - d) = (c - d)(a + x)
7. a(m + 2n) + bm + 2bn = a(m + 2n) + b(m + 2n) = (m+ 2n)(a + b)
8. x(3a + 1) + 6a + 2 = x(3a + 1) + 2(3a + 1) = (3a + 1)(x + 2)
9. m(4x − 1) + 12x – 3 = m(4x – 1) + 3(4x – 1) = (4x – 1)(m + 3)
10. y(5x − 2) − 15x + 6 = y(5x –2) – 3(5x – 2) = (5x – 2)(y – 3)

* Factorización completa.

1. ax + bx − ay – by = (a + b)(x – y)
2. 2xy + y − 6x – 3 = y(2x + 1) – 3(2x + 1) = (2x + 1)(y – 3)
3. 3mn + 15n − 4m –20 = 3n(m + 5) – 4(m + 5) = (m + 5)(3n – 4)
4. 2a2+6a-3ab-9b=2aa+3-3ba+3=a+3(2a-3b)
5. x+y2-3mx-3my2=x1-3m+y21-3m=1-3m(x+y2)
6. 6ab + 15a + 4b + 10 = 3a(2b + 5) + 2(2b + 5) = (2b + 5)(3a +2)
7. 12mn + 8m + 3n + 2 = 4m(3n + 2) + (3n + 2) = (3n + 2)(4m + 1)
8. 4 + 15xy + 5x + 12y = 5x(3y + 1) + 4(3y + 1) = (3y + 1)(5x + 4)
9. −6y − 9 + 15x + 10xy = 5x(2y + 3) – 3(2y + 3) =...