Guía de Ejercicios Algebra

Guía de Ejercicios

Algebra                                

1. Reduzca los términos semejantes en  las siguientes expresiones algebraicas:

1. 3x + 5x + x – 2x =
2. 5 ab – 4 a + 3 b + 3 ab  + ab – 5 a – 3 b =
3. –10 p2 + 4 q2 – 6 p2 + 2 q2 + 7p2q2 =
4. [pic 1] =
5. 0,2 a – ½ ab + a – ½ b + 0,4 ab – 0.5 b =

1. En las siguientes expresiones, elimine los paréntesis y luego reduzca los términos semejantes.

1. 2 a - ( 2 a – 3 b) + (4 a – b) =                        e) a – [ 2 a – (a + b) – 3b ] – 5 a =
2. 3x – ( x – 2) – (- x + 4) =                        f) 3x – [x – (2x – y) ] – (4x – y) + 3x =
3. [pic 2]                 
4. 4x – [ 2y – (x –y) ] – 3x =                g) – (2x2 – y2) + 3y2- x2 – [- 2x2 – (3x2 – y2) =

1. Realice las siguientes multiplicaciones:

1. –7 a · -2b · 5c =                        h) (3h + 2k – 3m) (2k –3h + 2m) =
2. 2 a3 b2 · -3 a b4 =                        i) [pic 3] =
3. 0,5x · 0,[pic 4] y · 0,4 x3y2 =                j) (0,2x + 1,3y) (5x – 3y)
4. [pic 5]=                k) (3x2 + 5xy3 + 8xy) (3x – 5y) =
5. x2y-3 · - x3 · -3x2 · y8 =                l) (5 a2b3 – 2 ab + 3 a2b4) (a – b) =
6. (3x + 2y) ( 3x + 7y) =                m) (5r – 2t + 4s) ( 3r + 4s – 2t) =
7. (a – b – c) (3 a + 2 b – 5 c)

1. Desarrolle los productos, elimine los paréntesis y reduzca los términos semejantes:

1. 3(x – 4) – (2x – 1) =                                e)  (x – 1) (x – 6) + (x + 7) (x – 3) =        
2. 3(a – b) – (a – 3b) – 5 (2a – 7b) =                        f)  (a3 – 3) (a3 – 8) + (a3 – 5) (a3 + 7) =
3. – 3 [ 2x (x – 1) + 3x (x – 3) – 2x (x – 3) ] =
4. 10 a – { - [ - (a2 – 1) + 5 ] – a (a – 2) } =                g) (x + 2y) (x + 3y) – (3x + 4y) (3x – 2y) =        

1. Desarrolle los siguientes productos notables:

1. (x + 5) (x – 5) =                                h) (0,2x2 – 0,3y3)2 =
2. (a –3) (a + 3) =                                i) (2x2y + 6xy2)2 =
3. (b2 + 7) (b2 – 7) =                        j) (x + 2)3 =
4. (6 x + 5y3) (6x – 5y3) =                        k) (5p – 1 )3 =
5. [pic 6] =                        l) (2 a3b + 3 ab3)3 =
6. (a – 3)2 =                                m) (2h + 3j + 4k)2 =
7. (3 a – 4)2 =                                n) (a – 5b + 3c)2 =

1. Reduzca las siguientes expresiones algebraicas.

1. (4 a2 – 5b)2 + (3 a2 – 2b) =
2. [pic 7]=
3. 7 (3m – n)2 – (m + n)2 – 2 ( 2m + n) (2m – n)=
4. (2x – 2y) (9x2 + 6xy + 4y2) – (27x3 – 8y3) =                                
5. (5x + 4y)3 – (5x + 4y) (25x2 – 20xy – 16y2) =

II.  FACTORIZAR

a) 15a+10b=                                                        b) 8m-12n=                        

c) 16a-20x=                                                        d) 24y-18z=                

e) 32x+24m=                                                        f) 0,5x-0,1y=

g) 0,25s+0,06t=                                                        h)1,5a-2,5b=                        

i) 0,6m+0,8n=                                                        j)  75x+100y=

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