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( 𝑎 + 𝑏)2
= 𝑎2
+ 2𝑎𝑏 + 𝑏2
( 𝑎 + 𝑏)2
+ ( 𝑎 − 𝑏)2
= 2(𝑎2
+ 𝑏2
)
( 𝑥 + 𝑎)( 𝑥 + 𝑏) = 𝑥2
+ ( 𝑎 + 𝑏) 𝑥 + 𝑎𝑏
( 𝑎 + 𝑏)( 𝑎2
− 𝑎𝑏 + 𝑏2) = 𝑎3
+ 𝑏3
Son los resultados de multiplicar dos o más polinomios,
en forma directa sin necesidad de aplicar la propiedad
distributiva.
TRINOMIO CUADRADO PERFECTO
( 𝑥 + 3)2
=
( 𝑥 − 4)2
=
(2𝑥 + 5)2
=
(3𝑥 − 6)2
=
IDENTIDADES DE LEGENDRE
( 𝑥 + 3)2
+ ( 𝑥 − 3)2
=
( 𝑥 + 4)2
− ( 𝑥 − 4)2
=
(2𝑚 + 𝑛)2
+ (2𝑚 − 𝑛)2
=
(√3 + √2)
2
+ (√3 − √2)
2
=
PRODUCTO DE DOS BINOMIOS CON TÉRMINO COMÚN
( 𝑥 + 3)( 𝑥 + 4) =
( 𝑥 − 4)( 𝑥 − 5) =
( 𝑥 + 2)( 𝑥 − 4) =
(3𝑥 + 5)(3𝑥 − 2) =
( 𝑚2
− 6)( 𝑚2
+ 2) =
DIFERENCIA DE CUADRADOS
( 𝑥 + 3)( 𝑥 − 3) =
( 𝑥 + 4)(4 − 𝑥) =
(3𝑚 + 5)(3𝑚 − 5) =
(2 − 4𝑛)(2 + 4𝑛) =
(5𝑥 − 1)(5𝑥 + 1) =
( 𝑥3
+ 7)( 𝑥3
− 7) =
( 𝑚 + 𝑛 + 𝑝)( 𝑚 + 𝑛 − 𝑝) =
CUBO DE UN BINOMIO
( 𝑥 + 2)3
=………………………………………………………………………………
………………………………………………………………………………
( 𝑥 − 4)3
=………………………………………………………………………………
………………………………………………………………………………
(2𝑥 + 1)3
=………………………………………………………………………………
………………………………………………………………………………
(4𝑥 − 2)3
=………………………………………………………………………………
………………………………………………………………………………
SUMA Y DIFERENCIA DE CUBOS
( 𝑥 + 2)( 𝑥2
− 2𝑥 + 4) =
( 𝑥 − 3)( 𝑥2
+ 3𝑥 + 9) =
( 𝑥 + 4)( 𝑥2
− 4𝑥 + 16) =
( 𝑥 − 5)( 𝑥2
+ 5𝑥 + 25) =
( √3
3
+ 1)( √9
3
− √3
3
+ 1) =
( 𝑥 − 5)( 𝑥2
+ 5𝑥 + 25) =
CUBO DE UN TRINOMIO
( 𝑎 − 𝑏)2
= 𝑎2
− 2𝑎𝑏 + 𝑏2
( 𝑎 + 𝑏)2
− ( 𝑎 − 𝑏)2
= 4𝑎𝑏
( 𝑎 + 𝑏)3
= 𝑎3
+ 𝑏3
+ 3𝑎𝑏(𝑎 + 𝑏)
( 𝑎 − 𝑏)3
= 𝑎3
− 𝑏3
− 3𝑎𝑏(𝑎 − 𝑏)
( 𝑎 − 𝑏)( 𝑎2
+ 𝑎𝑏 + 𝑏2 ) = 𝑎3
− 𝑏3
( 𝑎 + 𝑏 + 𝑐)3
= 𝑎3
+ 𝑏3
+ 𝑐3
+ 3( 𝑎 + 𝑏 + 𝑐)( 𝑎𝑏 + 𝑎𝑐 + 𝑏𝑐) − 3𝑎𝑏𝑐
( 𝑎 + 𝑏)( 𝑎 − 𝑏) = 𝑎2
− 𝑏2
PRODUCTOS NOTABLES
PRODUCTOS NOTABLES

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PRODUCTOS NOTABLES

  • 1. ( 𝑎 + 𝑏)2 = 𝑎2 + 2𝑎𝑏 + 𝑏2 ( 𝑎 + 𝑏)2 + ( 𝑎 − 𝑏)2 = 2(𝑎2 + 𝑏2 ) ( 𝑥 + 𝑎)( 𝑥 + 𝑏) = 𝑥2 + ( 𝑎 + 𝑏) 𝑥 + 𝑎𝑏 ( 𝑎 + 𝑏)( 𝑎2 − 𝑎𝑏 + 𝑏2) = 𝑎3 + 𝑏3 Son los resultados de multiplicar dos o más polinomios, en forma directa sin necesidad de aplicar la propiedad distributiva. TRINOMIO CUADRADO PERFECTO ( 𝑥 + 3)2 = ( 𝑥 − 4)2 = (2𝑥 + 5)2 = (3𝑥 − 6)2 = IDENTIDADES DE LEGENDRE ( 𝑥 + 3)2 + ( 𝑥 − 3)2 = ( 𝑥 + 4)2 − ( 𝑥 − 4)2 = (2𝑚 + 𝑛)2 + (2𝑚 − 𝑛)2 = (√3 + √2) 2 + (√3 − √2) 2 = PRODUCTO DE DOS BINOMIOS CON TÉRMINO COMÚN ( 𝑥 + 3)( 𝑥 + 4) = ( 𝑥 − 4)( 𝑥 − 5) = ( 𝑥 + 2)( 𝑥 − 4) = (3𝑥 + 5)(3𝑥 − 2) = ( 𝑚2 − 6)( 𝑚2 + 2) = DIFERENCIA DE CUADRADOS ( 𝑥 + 3)( 𝑥 − 3) = ( 𝑥 + 4)(4 − 𝑥) = (3𝑚 + 5)(3𝑚 − 5) = (2 − 4𝑛)(2 + 4𝑛) = (5𝑥 − 1)(5𝑥 + 1) = ( 𝑥3 + 7)( 𝑥3 − 7) = ( 𝑚 + 𝑛 + 𝑝)( 𝑚 + 𝑛 − 𝑝) = CUBO DE UN BINOMIO ( 𝑥 + 2)3 =……………………………………………………………………………… ……………………………………………………………………………… ( 𝑥 − 4)3 =……………………………………………………………………………… ……………………………………………………………………………… (2𝑥 + 1)3 =……………………………………………………………………………… ……………………………………………………………………………… (4𝑥 − 2)3 =……………………………………………………………………………… ……………………………………………………………………………… SUMA Y DIFERENCIA DE CUBOS ( 𝑥 + 2)( 𝑥2 − 2𝑥 + 4) = ( 𝑥 − 3)( 𝑥2 + 3𝑥 + 9) = ( 𝑥 + 4)( 𝑥2 − 4𝑥 + 16) = ( 𝑥 − 5)( 𝑥2 + 5𝑥 + 25) = ( √3 3 + 1)( √9 3 − √3 3 + 1) = ( 𝑥 − 5)( 𝑥2 + 5𝑥 + 25) = CUBO DE UN TRINOMIO ( 𝑎 − 𝑏)2 = 𝑎2 − 2𝑎𝑏 + 𝑏2 ( 𝑎 + 𝑏)2 − ( 𝑎 − 𝑏)2 = 4𝑎𝑏 ( 𝑎 + 𝑏)3 = 𝑎3 + 𝑏3 + 3𝑎𝑏(𝑎 + 𝑏) ( 𝑎 − 𝑏)3 = 𝑎3 − 𝑏3 − 3𝑎𝑏(𝑎 − 𝑏) ( 𝑎 − 𝑏)( 𝑎2 + 𝑎𝑏 + 𝑏2 ) = 𝑎3 − 𝑏3 ( 𝑎 + 𝑏 + 𝑐)3 = 𝑎3 + 𝑏3 + 𝑐3 + 3( 𝑎 + 𝑏 + 𝑐)( 𝑎𝑏 + 𝑎𝑐 + 𝑏𝑐) − 3𝑎𝑏𝑐 ( 𝑎 + 𝑏)( 𝑎 − 𝑏) = 𝑎2 − 𝑏2 PRODUCTOS NOTABLES