1
1
80. 1) a 9 6 a 3 a = a 9 ⋅ 1
1
−
4
1 2 + 9
a = a 9 ⋅ a 6⋅3 = a 9 5
1
34 5
2) b12 3 b 4 b = b12 ⋅ 3
1
63 4
1
b = b12 ⋅ b 3−4 = b12
1
1
6
−
2
−
1
−
+
1
= a3 ;
5 12
1
1
= b2 ; 1
4
2
−
4
−
1
−
1
1
4
3) ( ab−2 + (ab) 6 ) ab 4 = (a 3 b 3 + a 6 b 6 )a 6 b 6 = (a 6 b 6 + a 6 b 6 )a 6 b 6 = −
1
−
4
3
3
1
4
1 1 −
1 1 −
1
1
1
1
1
1
= a 6 b 6 (a 6 + b 6 )a 6 b 6 = a 6 6 b 6 6 (a 2 + b 2 ) = a 0b0 (a 2 + b 2 ) = a 2 + b 2 ; 2
2
1
1
1
1
4) ( 3 a + 3 b)(a 3 + b 3 − 3 ab) = (a 2 + b 2 )(a 3 + b 3 ) × 1
1
1
1
1
1
×((a 3 )2 − a 3 b 3 + (b 3 )2 ) = (a 3 )3 + (b 3 )3 = a + b . 1 1 1 1 81. 1) (1 − 2 b + b ) : (a 2 − b 2 )2 = 1 (a − 2 ab + b) : (a 2 − b 2 )2 =
a
a
a
1 1 = ( a − b )2 : ( a − b )2 = ; a a 1
1
1 1 1 1 1 1 2 2 − − a 3b + ) = (a 3 + b 3 ) : (a 3 − b 3 ⋅ (2a 3 b 3 + a 3 + b 3 ) = b a
2) (a 3 − b 3 ) : (2 + 3 1
1
1
1
1
1
1
1
1
1
= (a 3 + b 3 ) ⋅ a 3 ⋅ b 3 : : (a 3 + b 3 )2 = a 3 ⋅ b 3 : (a 3 + b 3 ) ; 1
3)
9
a4 − a4 1 4
−
−
5 4
a −a
b
−
1 2
3
− b2
1 2
b +b
=
1 − 2
1
8
1 4
4 4
a 4 (1 − a 4 )
−
1
4
b 2 (1 − b 2 )
−
1 − 2
a (1 − a )
2 2
=
b (b + 1)
1 − a2 − 1− a
2
b − 1 (1 − a )(1 + a ) (1 − b)(1 + b) = − = 1+ a −1+ b = a + b ; 1+ b 1+ a 1+ b −
1
3
−
1
1
−
2
1
−
1
−
1
2
a − a 2b a2 − a 3b a 2 − a 2b a 3 − a 3b a 2 (a 2 − b) 4) − = − 1 = 1 1 − 1 1 1 1 1 1 − − − 1 − a − 1b 6 a + a 3 b 1 − a 2 b 2 a 6 + a 3 b 2 a − 2 (a 2 − b 2 ) −
1
3
a 3 (a 3 − b)
−
−
1
3
a−b
=
1
1
1
1
a 2 + b2
1
−
1
1
1
=
1
1
1
(a 2 − b 2 )(a 2 + b 2 ) 1
a 2 + b2
1
1
−
a 2 − b2
1
1
1
1
( mn ) 7
2
3
2+ 3
7 +1
⋅y
( xy )
a 2 + b2
1
7
−b
3
=
= x
(mn ) (mn ) 7
3
2+ 3
⋅y
7
( xy)
7
⋅y
= =
(mn )
3
2
(mn ) (mn ) ( xy) ( xy)
7
⋅y 7
3
=
1 (mn )2
;
= y;
+ b 3 ) = ((a 2 )2 − (b 3 )2 ) = a 2 2 − b2 3 ; 4) (2a −0,5 − 1 b− 3 )( 1 b− 3 + 2a −0,5 ) = (2a −0,5 )2 − (1 b− 3 )2 = 4a −1 − 1 b−2 9 3 3 3
3) (a
1
(a 2 − b 2 )(a 2 + b 2 )
−a 2 + b 2 = 2b 2 = 2 b .
3 82. 1) m n
2) x
1
a 2 − b2
a 3 (a 6 − b 2 )
1
a−b
−
)(a
2
26
www.5balls.ru
3
.
=