The document contains examples of algebraic operations involving multiplication and division of polynomials and terms. Some key examples include: - Simplifying expressions like (x + 2y + (x - y)) by distributing terms - Combining like terms, such as 4m - 2n + 3 - (-m + n) + (2m - n) = 4m - 2n - 3 + (-m + n) - (2m - n) - Multiplying polynomials following standard order of operations, such as a2b3 • 3a2x = 3a4b3x - Dividing polynomials results in subtraction of exponents, like -xmync • -xmyncx = -

1. EJERCICIO 34
1. x + 2 y + ( x − y ) 6. − 2a + (− 3a + b)
[
= x − − 2 y − (x − y) ] [
= − 2a − (− 3a + b) ]
2. 4m − 2n + 3 − (− m + n) + (2m − n)
[
= 4m − 2n − 3 + (− m + n) − (2m − n) ]
2
(
7. 2 x + 3xy − y + xy + − x + y
2
) ( 2 2
)
[
= − − 2 x 2 − 3xy + ( y 2 + xy) − (− x 2 + y 2 ) ]
3. x − 3xy + x − xy + y
2
[( ) ]
2 2
= x2 − {3xy − [( x − xy) + y ] }
2 2
8. x 3 − − 3x 2 + 4x − 2
[ ]
4. x 3 − 3x 2 + − 4 x + 2 − 3x − 2 x + 3 ( ) = − − x 3 + − 3x 2 + 4 x − 2
{ }
[ [ ]
= x 3 − 3x 2 − − 4 x + 2 + 3x + (2 x + 3) ]
{
[ ( )] }
5. 2a + 3b − − 2a + a + b − a
9. [m − (3m + 2m + 3)]+ (− 2m + 3)
4 2
= − {− [ m − (3m + 2m + 3)] − (− 2m + 3)}
= 2a − [− 3b + {− 2a + [a + (b − a )] }]
4 2
EJERCICIO 35
17. ambn ⋅− ab = − am + 1bn + 1
1. 2 ⋅ − 3 = − 6 18. − 5ambn ⋅− 6a 2b3 x = 30am + 2bn + 3 x
2. − 4 ⋅− 8 = 32 19. xmync ⋅ − xmync x = − xm + myn + nc1+ x = − x 2my 2nc1+ x
3. − 15 ⋅16 = − 240
20. − mxna ⋅− 6m2n = 6mx + 2na + 1
4. ab ⋅− ab = − a1+ 1b1+ 1 = − a 2b2
5. 2x 2 ⋅− 3x = − 6x 2 + 1 = − 6x3
EJERCICIO 36
6. − 4a 2b ⋅ − ab 2 = 4a 2 + 1b1+ 2 = 4a 3b3
7. − 5x3 y ⋅ xy 2 = − 5x3 + 1y1+ 2 = − 5x 4 y 3 1. am ⋅ am + 1 = am + m + 1 = a 2m + 1
8. a 2b 3 ⋅ 3a 2 x = 3a 2 + 2b 3 x = 3a 4b3 x 2. − xa ⋅ − x a + 2 = x a + a + 2 = x 2a + 2
9. − 4m2 ⋅− 5mn2p = 20m2 + 1n2p = 20m3n2p 3. 4anb x ⋅− ab x + 1 = − 4an + 1b x + x + 1 = − 4an + 1b 2 x + 1
10. 5a y ⋅− 6x = − 30a x y
2 2 2 2
4. − a n + 1b n + 2 ⋅ a n + 2b n = − a n + 1+ n + 2 bn + 2 + n = − a 2n + 3b 2n + 2
11. − x2 y3 ⋅− 4y3 z4 = 4x2 y 3 + 3 z4 = 4x2 y 6 z4 5. − 3an + 4bn + 1 ⋅ − 4an + 2bn + 3 = 12a 2n + 6b2n + 4
12. abc ⋅ cd = abc1+ 1d = abc 2d 6. 3x 2 y 3 ⋅ 4x m + 1y m + 2 = 12x 2 + m + 1y 3 + m + 2 = 12xm + 3 y m + 5
13. − 15x 4 y3 ⋅− 16a 2 x 3 = 240a 2 x4 + 3 y 3 = 240a 2 x7 y 3 7. 4x a + 2b a + 4 ⋅ − 5xa + 5ba + 1 = − 20x 2a + 7b 2a + 5
14. 3a 2b3 ⋅− 4x 2 y = − 12a 2b3 x 2 y 8. ambnc ⋅ − amb 2n = − am + mbn + 2nc = − a 2mb3nc
15. 3a 2bx ⋅ 7b3 x 5 = 21a 2b1+ 3 x1+ 5 = 21a 2b 4 x 6 9. − xm + 1y a + 2 ⋅− 4xm − 3 y a − 5 c 2 = 4x2m − 2 y 2a − 3c 2
16. − 8m2n3 ⋅ − 9a 2mx 4 = 72a 2m2 + 1n3 x 4 = 72a 2m3n3 x 4 10. − 5manb − 1c ⋅− 7m2a − 3nb − 4 = 35m3a − 3n2b − 5c

2. EJERCICIO 37
3 m 2 3 1 3 m+1 3
1 2 4 3 1 4 4 5 2 8. − a ⋅ − ab3 = ⋅ am + 1b 3 = a b
1. a ⋅ a b = ⋅ a 5b = a b = a 5b 4 5 2 5 10
2 5 2 5 10 5
5 m n 3
3 2 7 2 3 9. a b ⋅− ab 2c
2. − m n ⋅− am 6 10
7 14
1 1 1
3 7 2 5 21 2 5 3 2 5 = − ⋅ am + 1 bn + 2 c = − am + 1bn + 2 c
= − ⋅− a m n= a m n= amn 2 2 4
7 14 98 14
2 x m +1 3 x −1 m
2 2 3 3 2 4 6 2 6 4 2 10. − a b ⋅− a b
3. x y ⋅− a x y = − a x y = − a2x 6y 4 9 5
3 5 15 5
2 1 2 x − 1 2m + 1 2 2 x − 1 2m + 1
= ⋅ a b = a b
1 3 4 4 3 2 4 3 5 5 1 3 5 5 3 5 15
4. − m n ⋅− a m n = amn = amn
8 5 40 10
3 m n 4 12 3m 2n 3 3m 2n
7 2 3 14 4 1 11. a b ⋅ − a 2mbn = − a b =− a b
5. − abc ⋅ a = − a bc = − a 4bc 8 5 40 10
8 7 56 4
2 x +1 x − 3 2 44 x − 3 2
3 3 4 5 3 1 12. − a b c ⋅− a b
6. − x y ⋅ − a 2by 5 = a 2bx 3y 9 = a 2bx 3 y 9 11 7
5 6 6 2 4 8
= 2 ⋅ a 2 x − 2b x − 1c 2 = a 2 x − 2b x − 1c 2
1 3 3 m+1 1 m+1 7 7
7. a ⋅ am = a = a
3 5 15 5
EJERCICIO 38 3 3 1 x a
8. − m ⋅− 5a 2m ⋅− am
5 10
1. a ⋅− 3a ⋅ a 2 = − 3a1+ 1+ 2 = − 3a 4 15 2 + x 3 +1+ a 3 x+2 a+4
=− a m =− a m
2. 3x 2 ⋅− x 3 y ⋅ − a 2 x = 3a 2 x 2 + 3 +1y = 3a 2 x 6 y 50 10
3. − m2n ⋅− 3m2 ⋅− 5mn3 = − 15m2 + 2 + 1n1+ 3 = − 15m5n4 9. 2a ⋅− a 2 ⋅ − 3a 3 ⋅ 4a = 24a1+ 2 + 3 + 1 = 24a7
4. 4a 2 ⋅− 5a 3 x 2 ⋅− ay 2 = 20a 2 + 3 +1x 2 y 2 = 20a 6 x 2 y2 10. − 3b 2 ⋅ − 4a 3b ⋅ ab ⋅− 5a 2 x
= − 60a 3 + 1+ 2 b 2 + 1+ 1x = − 60a 6b 4 x
5. −am ⋅ − 2ab ⋅− 3a 2b x = − 6am +1+ 2b1+ x = − 6am + 3b x + 1
1 3 2 2 3 6 2 + 4 3 +1 1 11. a mb x ⋅− a 2 ⋅ − 2ab ⋅− 3a 2 x
6. x ⋅− a x ⋅− a 4m = a x m = a 6 x 4m
2 3 5 30 5 = − 6a m + 2 + 1+ 2b x + 1x = − 6am + 5b x + 1x
2 m 3 2 4 1 2 3 10 3 3 2
7. a ⋅ a b ⋅− 3a 4b x + 1 12. − x y ⋅− xy 2 ⋅− x ⋅− x y
3 4 2 5 3 4
18 m + 2 + 4 4 + x + 1 3 6 2 + 1+ 3 + 2 1+ 2 + 1 3 8 4
=− a b = − a m + 6b x + 5 = x y = x y
12 2 8 4
EJERCICIO 39
4. a − 4a + 6a
3 2
2. 8x 2 y − 3y 2 3. x − 4x + 3
2
1. 3x 3 − x 2
− 2x 2ax 3 − 2x 3ab
− 6x + 2x
4 3
16ax 5 y − 6ax 3 y 2 − 2x 3 + 8 x 2 − 6 x 3a 4b − 12a 3b + 18a 2b