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1) Suma de monomios
a) - 5 x y + 9 x y + (-5 x y)=
= - 5 x y + 9 x y + -5 x y
= -xy
b) - 2 x2 y + 7x2 y + (-3x2 y) + 7x2 y =
- 2 x2 y + 7x2 y - 3x2 y + 7x2 y =
= 9x2 y
c) - (-32 a3 b3) + 17a3 b3 + 15a3b3 =

32 a3 b3 + 17a3 b3 + 15a3b3 =a
= 64 a3 b3

2) Suma de polinomios.
a) (a3 + 4) + (a2+ 5a + 1) + (3a3 + a2 – 3 a) =
a3 + 4 + a2+ 5a + 1 + 3a3 + a2 – 3 a ==4 a3 + 2a2+ 2a + 5
b) (-5a + 8b –7d) + (3c – 5b – 4d) =
-5a + 8b –7d + 3c – 5b – 4d =
=-5a + 3b+3c-11d
d) (4 m2 – mn + 3n2) + (-3m2 + 5 mn – 2n2) =
4 m2 – mn + 3n2 - 3m2 + 5 mn – 2n2 =
=m2 + 4mn + n2


3) Resta de monomios
a) 38 ab – (-8 ab) =
=38 ab +8 ab
= 46ab
b) –17 x – (-3 x) =
= -17 x + 3 x
= -14x
c) –8cg2 – (16 cg2) =
–8cg2 – 16 cg2 =
=-24cg2
4) Resta de polinomios
a) (6x2 – 6x3 + 5x) – (-4 + 6x2 – 3x3) =
6x2 – 6x3 + 5x + 4 - 6x2 + 3x3 =
= 3x3 + 5x + 4
b) (4x + 8y – 9z) – (-5x +y –z)=
4x + 8y – 9z + 5x - y + z)=
=9x+7y-8z
c) -(-5x + 7x3 – 4 + 2 x2) – (-9 + 3x -2x2 – 5x3) =
= 5x - 7x3 + 4 - 2 x2 + 9 - 3x +2x2 + 5x3) =
= - 2x3 + 2x+13
5) Sumas y restas combinadas
a) (3x3 – 5x2 +4x -8) – (-7x + 9x3- 8 + 5x2) + (-7 + 8x – 4x3) =
3x3 – 5x2 + 4x -8
-9x3 _ 5x2 + 7x +8
–4x3 + 8x -7
_____________________
= 10x3 + 19x -7

b) -[-5 x3 + (3x2 –2x3 + 4 - 5 x2)] =
=-[-5 x3 + 3x2 –2x3 + 4 - 5 x2] =
=-[-7 x3 - 2x2 + 4 ]
= 7 x3 + 2x2 - 4
c) -5x2 – [+4a – 7x – (-4a -3b)] =
=-5x2 – [+4a – 7x + 4a +3b]
=-5x2 – 4a + 7x –4a -3b
=-5x2 + 7x – 8a -3b
e) –[- (-8x + 5y – 4z)] – [- 4 x – (-7y –2z)] =

= –[+ 8x - 5y + 4z] – [- 4 x +7y + 2z] =
= –8x + 5y – 4z + 4 x -7y –2z =
= - 4x – 2y- 6z


6) Multiplicación de monomios
a) (5x) (-4x2)
= -20 x3
b) (-3x2y)(xy2)(- 7ay)
= 21x3 y4 a
c) (3 x y)(- ab )(-5ab x3y2) =
=(-3 xyab )(-5ab x3y2)
= 15 x4 y3 a2 b2
d) (-3xy)2 (5y2) (2x2 y3) ==(9x2 y2 )(5y2) (2x2 y3)
= 9x4 y7
f) (2x3 y1/2z) (-4x y 3/2x2) =
= -8x6 y2 z
7) Mulplicación de monomios por polinomios
a) (-2x) (5x2 –3x + 4) =
= - 10x3 + 6x2 _ 8x
b) (-3ab) (2a – 3b + 4a2b) =
= - 6a2 b +9ab2 _ 12a3 b2
c) (25xy3) (-2x1/2 y-2+ 3x3y –5y) =
= -50x3/2y +75x4 y4 – 125xy4


d) (3x) (2x2 + 4x-3) =
= 6x3 + 12x2 – 9x
8) Multiplicación de polinomios
a)(2 a – 3b) (5c + 4d) =
= 10ac+ 8ad-15bc-12bd
b) (6 x –3) (x2-4x+5) =
= 6x3 - 24x2 +30x – 3x2 +12x-15
c) (x2+3xy + 6)(2x2+ xy +2) =
= 2x4+ x3 y+2x2+6 x2 y + 3x2 y2 + 6xy +12 x2 +6xy+12
= 2x4+ x3 y+14x2+6 x2 y + 3x2 y2 + 12xy +12
d) (a2-2 ab + b2) (a2 + 2ab) =
= a4-2 a3b -2a3 b- 4a2 b2 + a2 b2 + 2ab3
= a4 _ 3a2 b2+ 2ab3
9) División de monomios
a) –12x3 ÷ 4x2 =
=-3 x3-2
= -3x

= 8 c2 d 3 / a2

c) +a5 b2 c ÷ - ab =
= -a4 bc
d) a10 b6c7 ÷ ab6c4 =
= a9 c3
10) División de un polinomio entre un monomio
a) (3a3 + 6a) ÷ a2 =
= 3a + 6/a
= 3ª+ 6a-1
b) (5 a 2 + 25 a4 15 a3) ÷ (- 5 a) =

= -a -5a3 + 3a2
c) (35 a3 bc – 25 a2 b3 c – 15 a3 b3 c3) ÷ (5 a3 b3 c3) =

= 35 a3 bc /5a3 b3 c3 – 25a2 b3c / 5a3 b3 c3 - 15 a3 b3c3 /5 a3 b3 c3
= 7/ b2 c2 - 5/ ac2 - 3

11) Trinomio cuadrado perfecto.
a) 4x2-20xy+25y2 =
=( 2x – 54)2
b) 25x2+30x+9 =
= (5x +3)2
d) 3a3+24a2b+48ab2 =
= 3ª (a2 +8ab+16 b2)
= 3ª (a+4b)2
12) Trinomio de la forma x2 + bx + c
a) x2+5x+6 =
= (x+3) (x+2)
b) x2+2x-15 =
= (x-3) (x +5)
c) a2-13a+40 =
d) m2-11m-12 =
= (m-12) (m+1)
13) Binomio cuadradoperfecto
a) (3 + x)2 =
=32 + 2(3) x + x2
= 9 + 6x + x2
b) (x-3)2=

= x2 - 2(x)(3) + 32
= x2 – 6x +9
c) (2x-4)2 =
= (2x2) – 2 (2x) (4)+ 42
= 4x2 – 8x +16
d) (5x2+3a)2 =
= (5 x2 )2 + 2 (5x2) ( 3a) +(3a)2
= 25x4 +30x2a + 9a2
e) (a+b)2 =
= (a+b) (a+b)
= a2 + 2ab+ b2
f) (-7a2b–2b)2 =
=-[(7 a2 b+ 2b)2]
=-[(7 a2 b)2+ 2(7a2 b) (2b)+ (2b)2]
=-[49a4 b+ 28a2 b2 + 4b2]


14) Cubo...