1103425
Description
Mind Map by Juan David Molina, updated more than 1 year ago
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Created by Juan David Molina
over 10 years ago
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FACTORIZACION
- Caso I: Factor Común
- ax+bx = x(a+b
- ax+bx = x(a+b
- Caso II: Factor común por agrupación
- ax+bx-ay-by =
(ax+bx)-(ay+by) =
x(a+b) - y(a+b) =
(a+b)(x-y)
- ax+bx-ay-by =
(ax+bx)-(ay+by) =
x(a+b) - y(a+b) =
(a+b)(x-y)
- Caso III: Trinomio cuadrado
perfecto
- a 2 +2ab+b2 =
(a+b)2
- a 2 +2ab+b2 =
(a+b)2
- Caso IV: Diferencia de cuadrados
- a 2 – b2 = (a – b) (a + b)
- a 2 – b2 = (a – b) (a + b)
- CasoV: Trinomio cuadrado
por Adición y Sustracción
- x 4 + x2 y 2 + y4 =(x2 + y2 ) 2 – x2 y 2 + x2 y
2 =[(x2 + y2 ) – xy] [(x2 + y2 ) + xy] +2x2 y 2
=[ x2 + y2 – xy] [ x2 + y2 + xy] =[ x2 – xy + y2 ]
[ x2 + xy + y2 ]
- x 4 + x2 y 2 + y4 =(x2 + y2 ) 2 – x2 y 2 + x2 y
2 =[(x2 + y2 ) – xy] [(x2 + y2 ) + xy] +2x2 y 2
=[ x2 + y2 – xy] [ x2 + y2 + xy] =[ x2 – xy + y2 ]
[ x2 + xy + y2 ]
- Caso VI: Trinomio de la forma x2 + bx + c
- • x 2 + 5x + 6 =
(x + 3)(x + 2) • x
2 – 7x + 6 = (x -
6)(x - 1) • x 2 –
3x – 10 = (x –
5)(x + 2) • x 2 +
x – 20 = (x +
5)(x - 4)
- • x 2 + 5x + 6 =
(x + 3)(x + 2) • x
2 – 7x + 6 = (x -
6)(x - 1) • x 2 –
3x – 10 = (x –
5)(x + 2) • x 2 +
x – 20 = (x +
5)(x - 4)
- Caso VII: Trinomio de la Forma ax2
+ bx + c
- 10 x2 – 9 x + 2 = (5x – 2)
(2x – 1) 5x -2 = -4x 2x -1 =
-5x . -9x
- 10 x2 – 9 x + 2 = (5x – 2)
(2x – 1) 5x -2 = -4x 2x -1 =
-5x . -9x
- Caso VIII: Cubo Perfecto de un Binomio
- a 3 + 3 a2 b + 3ab2
+ b3 = (a + b)3
- a 3 + 3 a2 b + 3ab2
+ b3 = (a + b)3
- Caso IX: Suma o Diferencia de Cubos
- x 3 + y3 = (x + y)(x2 – xy + y2 )
- x 3 + y3 = (x + y)(x2 – xy + y2 )
- Caso X: Suma o Diferencia de dos
Potencias Iguales
- • x 5 + y5 = (x + y)(x4 – x3 y + x2 y 2 – xy3 + y4 )
- • x 5 + y5 = (x + y)(x4 – x3 y + x2 y 2 – xy3 + y4 )
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