The document discusses algebraic expressions including: - Adding, subtracting, and finding the numerical value of expressions - Factorizing expressions using the product of sums/differences and factoring trinomials - Simplifying fractions through factoring the numerator and denominator - Performing operations like multiplication, division, addition and subtraction on fractions It also covers factorizing algebraic expressions using Ruffini's method.

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