Prod Notables
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Guía 1º Medio: Productos Notables
1. 2. 3. 4.
(1 + 3x ) = ( 7a b + 5x ) = ( a − b )( a + b ) = 4 2
4 2
2 3
3
2
3
2
(1 − 8 xy ) ⋅ (1 + 8 xy ) =
(a
)(
x +1
)
− 2b x −1 2b x −1 + a x +1 = 6. ( x + y + z )( x + y − z ) = 5.
(a 2 − 2b)3 = 8. ( x 3 + 6 )( x 3 − 8) = 9. ( x 3 y 3 − 6 )( x 3 y 3 + 6 ) = 10. (5a x +1 − 7 )(5a x +1 − 4 ) = 7.
2 3
6 4 −3 2 11. a b c + 11ab =
(
12. 5x 2 − 3
(
)3 =
)
13. ( x − 1) x 2 + x + 1 =
(
)
14. ( 2 + y ) 4 − 2 y + y 2 =
( )( 16. ( x a +1 − 8)( x a +1 + 9 ) =
)
15. a 2n b m − 2 x 3 y a a 2n b m + 2 x 3 y a =
x +1 m b − 17. 3 7 a
(
)(
1 − 7 − 2 1 b c 3 7 a x +1b m + b − 7 c − 2 = 5 5
)
18. a 2 b 2 − 1 a 2 b 2 + 7 =
(
)
19. ( 5 − ab ) 25 + 5ab + a 2 b 2 =
( )2 = 21. (3a x + y − 2 )(3a x + y − 5) = 20. 2mn 2 + 3m −1n − 3
2
1 2 22. a 2 b − x 3 y 4 = 5 3
(
)(
)
23. m 2 − m + n n + m + m 2 = 24. ( 2a − 3b + c ) 2 =
(
)(
)
25. x 2 y −3 z −6 − 5a 3b 7 c x 2 y −3 z −6 + 5a 3b 7 c =
1. 2. 3. 4.
(1 + 3x ) = ( 7a b + 5x ) = ( a − b )( a + b ) = 4 2
4 2
2 3
3
2
3
2
(1 − 8 xy ) ⋅ (1 + 8 xy ) =
(a
)(
x +1
)
− 2b x −1 2b x −1 + a x +1 = 6. ( x + y + z )( x + y − z ) = 5.
(a 2 − 2b)3 = 8. ( x 3 + 6 )( x 3 − 8) = 9. ( x 3 y 3 − 6 )( x 3 y 3 + 6 ) = 10. (5a x +1 − 7 )(5a x +1 − 4 ) = 7.
2 3
6 4 −3 2 11. a b c + 11ab =
(
12. 5x 2 − 3
(
)3 =
)
13. ( x − 1) x 2 + x + 1 =
(
)
14. ( 2 + y ) 4 − 2 y + y 2 =
( )( 16. ( x a +1 − 8)( x a +1 + 9 ) =
)
15. a 2n b m − 2 x 3 y a a 2n b m + 2 x 3 y a =
x +1 m b − 17. 3 7 a
(
)(
1 − 7 − 2 1 b c 3 7 a x +1b m + b − 7 c − 2 = 5 5
)
18. a 2 b 2 − 1 a 2 b 2 + 7 =
(
)
19. ( 5 − ab ) 25 + 5ab + a 2 b 2 =
( )2 = 21. (3a x + y − 2 )(3a x + y − 5) = 20. 2mn 2 + 3m −1n − 3
2
1 2 22. a 2 b − x 3 y 4 = 5 3
(
)(
)
23. m 2 − m + n n + m + m 2 = 24. ( 2a − 3b + c ) 2 =
(
)(
)
25. x 2 y −3 z −6 − 5a 3b 7 c x 2 y −3 z −6 + 5a 3b 7 c =
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