1) Efetue as operações com monômios:
a) a2 + 6a2 – 2a2
b) 5y2 – (- 4y2 + 7y2) + (
- y2 + 9y2- 11y2)
c) ( - 7x)
. (-2x)
d) ( -5a4bc3)
.( -b2c) . (+4a2c)
e) x7
: x2
f) y5
: y3
Respostas:
a) a2 + 6a2 – 2a2 adicionar –se ou subtrair –se os coeficientes e repete a parte literal.
(1 + 6 – 2 ) a2= 5a2
b) 5y2
– (- 4y2 + 7y2) + ( - y2 + 9y2- 112)
5y2 –
( 3y2) + ( - 3y2) =
5y2 – 3y2
- 3y2= - y2
c) ( - 7x) .
(-2x) multiplica-se os coeficientes entre si e a parte literal entre si.
( - 7) . (-2) ( -x ) . (-x)
( +14 ) ( x2) = 14x2
d) ( -5a4bc3) .( -b2c) .
(+4a2c)
(-5).(-1) . (4) . ( a4) . ( a2 ) . (b
) . (b2) . ( c3 ) . ( c). (c) =
(20 ) . ( a6 ) . ( b3 ) . ( c5
)= 20a6 b3 c5
e) x7 : x2 repete-se a base e
subtrai-se os expoentes:
x7 – 2 = x5
f) y5
: y3
y5-3
= y2
2) Efetue as operações com polinômios:
a) (15x -7y + 4z) + (-8y + 3z – 9x)
b) (3x3 –
3x2y + 5xy2 – 6y3 ) + ( 7x2y – 5x3
+ y3 – 6xy2)
c) ( x + 7 ) . (
x + 5)
d) (y - 6) . (y +
5)
e) ( -28x4 + 8x2) : ( 4x2)
f)( 6x6 -5x4 + 3x3 – 9x2):
( 3x2)
g) (6x5
+ 3x4 – 13x3 – 4x2 + 5x + 3) : ( 3x3
– 2x -1 )
Respostas:
a) (15x -7y + 4z)
+ (-8y + 3z – 9x)
(15x – 9x ) + (
-7y – 8y )+ ( 4z + 3z) =
(6x ) + ( -15y)+
( 7z)=
6x -15y + 7z
b) (3x3 – 3x2y + 5xy2 – 6y3
) + ( 7x2y
– 5x3 + y3 – 6xy2)
(3x3 –5x3 ) + ( -3x2y+ 7x2y)
+ ( 5xy2-6xy2 ) + ( -6y3 + y3)=
( –2x3 ) + ( 4x2y) + ( - xy2 ) + ( -5y3
)=
–2x3 + 4x2y - xy2
-5y3
c) ( x + 7 ) . ( x + 5)
( x . x) + (x . 5) + (7 . x ) + (7 . 5)=
( x2)
+ (5x) + (7x ) + (35)=
x2 + 12x + 35
d) (y - 6) . (y +
5)
(y . y) + (y . 5
) + ( -6 .y) + (- 6 . 5)
(y2) +
( 5y ) + ( -6 y) + (-30)
(y2) +
5y -6 y -30
y2 - y -30
e) ( -28x4
+ 8x2) : ( 4x2)
-28x4 + 8x2
4x2 4x2
-7x2 + 2
g) (6x5
+ 3x4 – 13x3 – 4x2 + 5x + 3) : ( 3x3
– 2x -1 )
6x5
+ 3x4 – 13x3 – 4x2 + 5x + 3 [3x3
– 2x – 1
-6x5 +4x3 +2x2 2x2
+ x – 3
3x4 -9x3 -2x2 + 5x +
3
-3x4 + 2x2 + x
-9x3 + 6x
+3
9x3 -6x
- 3
0
