Ejercicios de Expresiones algebraicas

1. REPUBLICA BOLIVARIANA DE VENEZUELA
MINISTERIO DEL PODER POPULAR PARA LA EDUCACIÓN
UNIVERSIDAD POLITÉCNICA TERRITORIAL DE LARA
ANDRÉS ELOY BLANCO
BARQUISIMETO, EDO-LARA
Expresiones Algebraicas ,
Factorización y Radicación
Eiber Mendoza C.I: v.29.506.223
Pablo Peraza C.I: v-29.795.117
PNF Higiene y Seguridad Laboral

2. • Expresiones algébricas •
• Suma
• Resta
•Valor numérico
 4x+3y+z ; 2x+3y-2z =
=(4x+3y+z) + (2x+3y-2z)
=(4+2) x + (3+3) y + (1-
2)z
=6x+6y-z
 6x + 3x =
=9x
 9xyz – 5xyz =
=4xyz
 4x + 3y + z ; 2x +3y -
2z =
=(4x + 3y + z) - (2x + 3y
- 2z)
= 4x + 3y+z – 2x +3y –
2z
=(4-2) x + (3+3) y + (1-
2)z
=2x+6y-z
3x - 2x + 1 ; X= -2
= 3. (-2) -2. (-2) + 1
= -3. (-4) – 4. (-4) + 3
= 3. 4 – 2. (-2) +1
= -3. 16 + 16 + 3
= 12 + 4 + 1
= -48 + 19
= 17
-3x – 4x +3 ; x= -4
= -3. (-4) – 4. (-4) + 3
= 3. 4 – 2. (-2) +1
= -3. 16 + 16 + 3
= 12 + 4 + 1
= -48 + 19
= 17
= -29
2
2
2
2

3. • Expresiones algébricas •
•Factorización por producto Notable
 Ay - 2ay - 6by + 3bx
= (ay – 2ay) + (-6by + 3by)
= (1 – 2)ay + (-6 + 3)by
= (-1ay) . (-3by)
 x y z – 3x y z + 5x y z
= ( X . Y . Z ) -3(X . Y . Z ) + 5(X . Y . Z )
= X . Y . Z -
•Simplificación de fracciones
X - 16 = ( X – 4) . ( X
+ 4)
X - 8X +16 ( X -4)
 X - 16
X - 8X +16
X - 3X - 4 = (X – 4) . (X + 1)
X - X – 12 (X – 4) . (X + 3)
= ( X+ 1)
( X + 3)
 X -3X – 4
X – X - 12
2 2
2
2
2
2 2 2
2
3 3
3
3
3
2
2
2
2
2
2 2
2
2
2
2

4. • Expresiones algébricas •
• Suma y resta de fracciones
 X + X + 1
X – 1 (X- 1 )
= X . (X -1) + (X – 1) . (X + 1)
(X – 1) . (X – 1)
= X . ( X +1) + ( X – 1)
( x – 1 ) . (x + 1)
= X + ( x – 1 )
( x – 1)
 X y + X
9x – y x – x + 1
= ( x. y) . (x – x+1) + (x) . (9x – y )
(9x – y ) . (x – x + 1)
= (X . Y) + x
2 2
2 2
2 2
2
2 2
2
2 2 2
2 2 2
2 2 2
3
3

5. • Expresiones algébricas •
•Multiplicación •División
 2 x +2 x ; X - 3x
2 X x -2x – 3
= 2 x + 2 . X . X –
3x
2 x X –
2x-3
= (2 x +2 x ) . (X – 3 x
)
(2 x ) . (X – 2x – 3)
= X ( 2 x + 2) . (X -3 x )
X (2 x ) . (x – 2) . (x +
1)
= X (2 x + 2 ) . (x – 3 x
)
X ( 2 X ) . (x – 3 x )
= X ( 2 x + 2)
X ( 2 x )
 (X – y) , X + X + 1
X – 1 (X – y)
= (X – Y ) . (X + X + 1)
(X – 1) . ( x – y )
=( X – Y ).x (X + 1).(X –
1)
(X – 1) . (X – Y )
= ( x – y ) . ( x – 1)
(x – 1) ( x – y )
= ( x – y )
( x – y )
= x+ y
2
2
2
2
2
2
2
2
2 2
2 2
2
2
2
2
2
2
2
2
2 2
2 2
2 2
2 2
3
3
3
3
3
3
3
3
3 3 3
3
3 3

6. • División Fracciones Algebraicas
 3 a
5 a
a + 6 a b + 9 b a
b + 3 a b
/
+ -
( 3 a ) . ( a b + 3 a b
)
( 5 a ) . ( a + 6 a b +
9 b )
=
=
3 a b + 9 a b
5 a + 30 a b + 45 a b
=
12 a b
80 a b
= = 12 a
80 a
12 a a
80
= =
12 a
80
 ( x - 7x + 5 ) / ( x -
3)
• Factorización por el Método Ruffini
 (x – x + 2x -2) / (x+1)
2
2
3
X-3=0
X=3
1 -7 5
3 -12
1 -4 -7
3
C(X)= -
4
R(x)= -
7
1 -2 4 -6
-1 2 -4
1 -1 2 -2
-1
1 -7 5

7.  ( x - 7x + 5 ) / ( x -
3)
• Factorización por el Método Ruffini
 (x – x + 2x -2) / (x+1)
2
2
3
X-3=0
X=3
1 -7 5
3 -12
1 -4 -7
3
C(X)= -
4
R(x)= -
7
X+1=0
X= -1
1 -2 4 -6
-1 2 -4
1 -1 2 -2
-1
C(X)= x -2x +4
R(x)= -6
2
1 -7 5