contaduria

Factorizar completamente, si es posible:
1. (a + 2b) + ma + 2bm
Desarrollo
(a + 2b) + ma + 2bm = (a + 2b) + m(a + 2b) Factorcomun
= (a + 2b)(1 + m) Factor comun
2. 2xz + 2ax + z + a
Desarrollo
2xz + 2ax + z + a = 2x(z + a) + z + a Factor comun
=2x(z + a) + (z + a) Agrupando terminos
= (z + a)(2x + 1) Factor comun
3. 3(a 􀀀 b)2 + 5(a 􀀀 b)
Desarrollo
3(a 􀀀 b)2 + 5(a 􀀀b) = (a 􀀀 b)(3(a 􀀀 b) + 5) Factor comun
= (a 􀀀 b)(3a 􀀀 3b + 5) Organizando terminos
4. (c + 3)2 + 5c + 15 + 2ac + 6aDesarrollo
(c + 3)2 + 5c + 15 + 2ac + 6a = (c + 3)2 + (5c + 15) + (2ac + 6a) Agrupando terminos
= (c + 3)2 + 5(c + 3) + 2a(c + 3)Factor comun (en cada termino)
= (c + 3)((c + 3) + 5 + 2a) Factor comun
= (c + 3)(c + 3 + 5 + 2a)
= (c + 3)(2a + c + 8)Organizando terminos
5. (2b + 2c)2 + b + c
Desarrollo
(2b + 2c)2 + b + c = (2(b + c))2 + b + c Factor comun
= 4(b + c)2 + (b +c) Organizando y agrupando terminos
= (b + c)(4(b + c) + 1) Factor comun
= (b + c)(4b + 4c + 1) Organizando terminos
6. (am+ 3an)3 + (2m + 6n)2
Desarrollo
(am + 3an)3 + (2m + 6n)2 = (a(m + 3n))3 + (2(m + 3n))2 Factor comun
= a3(m + 3n)3 + 4(m +3n)2 Organizando y agrupando terminos
= (m + 3n)2(a3(m + 3n) + 4) Factor comun
= (m + 3n)2(a3m + 3a3n + 4) Organizando terminos