1. EXPRESIONES ALGEBRAICAS 3° Año “C”
Resuelve las siguientes operaciones.
a) Adicciones y sustracciones:
1- (4 a
3
– ½ a + 2 + 2/3 a
2
) + (-3 a – 1/3 a
2
+ 2 a
3
) =
2- (3/5 c
2
– 2 c + 1/5) + (- 2 c
2
+ 1/3 c + ½) =
3- (-1/2 y
2
+ 3) + (-4/7 y
2
+ y
3
– 4/5) + (2 – 1/6 y
2
+ ½ y
3
) =
4- (3/2 a
2
– 2 a) - (- a + 2) =
5- (3/2 c
2
– 2 c + 1/5) – (- 2 c
2
+ 1/3 c + ½) =
6- (-4/3 y
2
+ y
3
– 4/5) - (2 – 1/3 y
2
+ ½ y
3
) =
7- ( -5mn
3
+ 1/3mn – 0,2m
2
n
3
) – (-2,5mn + 1/4m
2
n
3
-3/5mn
3
)=
8- (2,5xy – 0,25x
3
y
2
+ 3/8x
2
y) – ( 2/3x
2
y – 0,15xy + 10x
3
y
2
)=
9- (-1/2 xy
2
+ 3,2) + (-4/5xy
2
+ xy
3
– 4/5) - (2 – 1/6xy
2
+0,5xy3) =
b) Productos:
1- (3b - 4b
3
+ 5 b
2
) . (-2b
2
) =
2- ( 12 m
2
y – 30m
3
y
2
– m) . ( -3my
2
)=
3- (12 m
2
y– 2m
5
– m) . ( m – 2)=
4- (-1/2 y
2
+ 3) . (-4/3 y
2
+ y
3
– 4/5)=
5- (3/2 c
2
– 2 c + 1/5) . (- 2 c
2
+ 1/3 c + ½)=
6- (3/4 ab
2
– 2 a + ½) . (- 2 ab
2
+ 1/4 a + ½)=
7- (4/7 y
2
+ y
3
– 4/5) + (2y – 1/6 y
2
) =
8- (4 a
3
– ½ a + 2 + 2/3 a
2
) . (-3 a – 1/3 a
2
)=
c) Potencias:
1- (1/5 a b
4
c
5
)
3
=
2- ( 1/3 xz
3
y
6
)
4
=
3- (0,2mn
12
)
2
=
4- (-3 a
4
b
15
c
7
)
3
=
5- (5x
8
y
5
z
2
)
3
=
6- [( -1/2 ab
5
c
4
d
9
)
2
]
2
7- {[( -2 ab
2
c
4
d
5
)
2
]
0
}
3
=
d) Productos especiales:
1- (-3y – 4)
2
=
2- ( m – 2)
2
=
3- (-2 a
2
x – 1/3 ax
2
)
2
=
4- (a – 2b)
3
=
5- (2m + m
2
)
3
=
6- (1/2x – 2)
3
=
7- (y – 1/4). (y + 1/4) =
8- ( x – ½) . ( x + ½)=
9- (ab – 0,2) . (ab + 0,2)=
10-(m + 1/3n) . (m – 1/3n)=
e) Cocientes:
1- ( 12 m
2
y – 30m
3
y
2
– m) : ( -3my
2
)=
2- ( 22 m
2
y– 20m
5
– m) : ( m – 2)=
3- (2 – 1/6 y
2
+ ½ y
4
) : (y
2
+ y)=
4- (5a
3
–1/4a + 1 –2/3a
2
) : (2a – 3)=
5- (n
5
+ 4n
3
– 6) : (n + 2)=
6- (m
4
– 2m
2
+ 5) : (m – 2)=
7 - (x
3
– x + 3) : ( x – 5)=
8- (2x
6
– 3x + 2) : (x – ½)=
f) Regla de Ruffini. Aplicación.
1- (2x
4
– 4x
3
+ 1/3x
2
– 10x – 2) : (x – 2)=
2- (3x
3
- 10x
2
+ 5x – 1/5) : (x + 3)=
3- (0,2a
4
+ a
3
– 2) : (a + 3/2)=
4- ( 0,3m
4
– 0,1m – 2) : ( m – 0,2)=
5- (2x
6
– 3x + 2) : (x – ½)=
6- (x
3
– 3) : ( x – 5)=
g) Teorema del Resto. Aplicación.
1- (2x
4
– 5x
3
+ 1/2x
2
– 10x – 2) : (x – 1)=
2- (5x
3
+ 10x
2
+ 5x – 1/5) : (x + 5)=
3- (0,2a
4
+ a
3
– 2) : (a + 2/5)=
4- ( 0,5m
4
– 0,1m – 2) : ( m – 0,2)=
5- (x
6
– 3x + 2) : (x – ½)=
6- (x
3
– x + 3) : ( x – 5)=