Números reales. Propiedades de los números reales

Números reales

Propiedades de los números reales

Sección 1. Define qué propiedad de los números reales se usó en los siguientes problemas.

1. 2(x + y) = 2x + 2y                Distributiva
2. (x + 5) + y = y + (x + 5)                Conmutativa
3. 2(3y) = (2*3)y                        Asociativa
4. [pic 1][pic 2]                        
5. 5(b – a) = (a – b)(-5)
6. Y + (x + y) = (y + x) + y                Conmutativa
7. 8 – y = 8 + (-y)
8. 5(4 + 7) = 5(7 + 4)                Asociativa
9. (8 + a)b = 8b + ab                Distributiva
10. (-1)[-3 + 4] = (-1)(-3) + (-1)(4)        Distributiva

Sección 2. Utilizando las propiedades de los números reales, demuestra que los siguientes enunciados son verdaderos.

1. 2x(y – 7) = 2xy – 14x
2. (a – b) + c = a + (c – b)
3. (x + y)(2) = 2x + 2y
4. 2[27 + (x + y)] = 2[(y + 27) + x]
5. x[(2y + 1) + 3] = 2xy + 4x

Sección 3. Simplifica las siguientes expresiones, si es que se puede:

1. -2 + (-4)=                 -6
2. 6 + (-4)=                 2
3. 7 – (-4)=                 11
4. –a – (-b)=                 -a+b
5. 7(-9)=                         -63
6. 19(-1)=                         -19
7. -(-6 + x)=                 6-x
8. -12(x – y)=                 -12x+12y
9. -3 ÷ 15=                 -3(1/15)
10. (-a) ÷ (-b)=                 -a(1/-b)
11. 3[-2(3) + 6(2)]=                 18
12. (-12)(-12)=                (12)^2
13. 3(x – 4)=                 3x-12
14. –(x – 2)=                 -x+2
15. 8[pic 3][pic 4] =                         8/11
16. [pic 5][pic 6]=                         14x(21y)^-1
17. [pic 7][pic 8]=                         2/3x
18. (5a)[pic 9][pic 10]=                 7
19. [pic 11][pic 12]=                         7/yx
20. [pic 13][pic 14]=                        5/6
21. [pic 15][pic 16]=                        -1/5
22. [pic 17][pic 18]=                        x-y/√5
23. [pic 19][pic 20]=                        1/40
24. [pic 21][pic 22]=                        1/3m
25. [pic 23][pic 24]=                        Indefinido

Operaciones con expresiones algebraicas

Sección 4. Realiza las operaciones indicadas y simplifícalas hasta donde sea posible:

1. (8x – 4y + 2) + (3x + 2y + 5)=                        11x-2y+7
2. (8t2 – 6s2) + (4s2 – 2t2 +6)=                        6t^2-2s^2+6
3. ([pic 25][pic 26]=                        √a+5√3b-√c
4. (6x2 – 10xy + [pic 27][pic 28]) – (2z – xy + 4)=                6x^2-9xy-2z(-4+√2)
5. [pic 29][pic 30]=                        √2y-√3z
6. 3(3x + 3y - 7) – 3(8x – 2y + 2)=                        -18x+12y-27
7. 5(x2 – y2) + x(y – 3x) – 4y(2x + 7y)=                2x^2-33y^2-9xy
8. 2{3[3(x2 + 2) -2(x2 - 5)]}=                        6x^2+96
9. -5(4x2(2x + 2) – 2(x2 – (5 – 2x)))=                -40x^3-30x^2+20x-50
10. (x + 4)(x + 5)=                                        x^2+9x+20
11. (w + 2)(w - 5)=                                        w^2-3w-10
12. (2x + 3)(5x + 2)=                                10x^2+19x+6
13. (x + 2y)2=                                        x^2+4xy+4y^2
14. (x - 5)2                                                x^2-10x+25
15. ([pic 31][pic 32] + 5)2=                                        3x+10√(3x)+25
16. (2s - 1)(2s + 1)=                                4s^2-1
17. (x2 - 3)(x + 4)=                                        x^3+4x^2-3x-12
18. (x2 - 4)( 3x2 + 2x - 1)=                                3x^4+2x^3-13x^2-8x+4
19. x{2(x + 5)(x - 7) + 4[2x(x - 6)]}=                        10x^3-52x^2-70x
20. (x + y + 2)(3x + 2y - 4)=                         3x^2+2y^2+2x+5xy-8
21. (2ª + 3)3=                                        2^a+3+9
22. (2x - 3)3=                                        8x^3-48x^2+54x-27
23. [pic 33][pic 34]=                                                z-18
24. [pic 35][pic 36]=                                        
25. (x2 + 5x - 3)÷(x + 5)=                
26. (3x3 – 2x2 + x - 3) ÷ (x + 2)
27. x3 ÷ (x + 2)=                                        
28. (3x2 – 4x + 3) ÷ (3x + 2)=

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