FÓRMULAS NOTABLES. CADRADO DUN BINOMIO

(2 + x)² = 2² + 2(2)(x) + x²= 4 + 4x + x²

(3a – 5b)² = (3a)² - 2(3a)(5b) + (5b)²= 9a² - 30ab + 25b²

(x + y)² = x² + 2 (x)(y) + y²= x² + 2xy + y²

(p - q)² = p² - 2pq + q²

(2p + q)² = (2p)² + 2(2p)(q) + q²= 4p² + 4pq + q²

(3a + b)² = (3a)² + 2(3a)(b) + b²= 9a² + 6ab + b²

(2a - 3b)² = (2a)² - 2(2a)(3b) + (3b)²= 4a² - 12ab + 9b²

(x + 1)² = x² + 2(x)(1) + (1)²= x² + 2x + 1

(a - 6)² = (a)² - 2(a)(6) + (6)²= a² - 12a + 36

(x + 9)² = (x)² + 2(x)(9) + (9)²= x² + 18x + 81

(3p - 1)² = (3p)² - 2(3p)(1) + (1)²= 9p² - 6p + 1

(x + 5)² = (x)² + 3(x)(5) + (5)²= x² + 10x + 25

(6x – 5y)² = (6x)² - 2(6x)(5y) + (5y)²= 36x² - 60xy + 25y²

(2m – 1)² = (2m)² - 2(2m)(1) + (1)²= 4m² - 4m + 1

(4pq - 3q)² = (4pq)² - 2(4pq)(3q) + (3q)²= 16 p² q² – 24pq² + 9q²

FÓRMULAS NOTABLES. SUMA POR DIFERENCIA

(x + 2y)(x - 2y) = (x)² – (2y)² = x² – 4y²

(3a - b)(3a + b) = (3a)² - (b)² = 9a² - b²

(5x² - 3y)(5x² + 3y)= (5x)² – (3y)² =25x² - 9y²

(2x - 3xy)(2x + 3xy)= (2x)²–(3xy)²= 4x²- 9x²y²

(6a + 1)( 6a – 1) = (6a)² - (1)² = 36a ² - 1

SACAR FACTOR COMUN

36x4 - 48x6 - 72x3 + 60x5 = 12x3. (3x - 4x3 - 6 + 5x2)

9x2ab - 3xa2b3 + x2az = xa. (9xb - 3ab2 + xz)

9x3 + 24x2 + 16x= ( )16249· 2 ++ xxx

2x4 – 6x3 – 6x2= ( )33·2 22 −− xxx

OPERACIONS POLINOMIOS

1. (x2 – x – 1) – (x – 2) (4x – 6) = 14122 2 −+− xx

2. 6x3 – 3x (4 – 2x – x2) + 5x (x – 3) = xxx 27119 23 −+

3. (2x – 3)2 + (1 – x) (x + 1) – (3x2 + 2x – 5) = 1514 +− x

FACTORIZACIÓN POLINOMIOS

a) 9x5 – 6x4 + x3 = ( )23 13· −xx

b) 5x3 – 5x = ( ) ( )1·1·5 −+ xxx

c) 4x4 – 12x² + 9 = ( )22 32 −x

d) 3x² + 30x + 75 = ( )25·3 +x

e) 9x3 + 24x2 + 16x = ( )16249· 2 ++ xxx

f) 2x2 + 4x – 6 = ( ) ( )1·3·2 −+ xx

g) 2x2 + 7x – 4 = ( )4·2

1·2 +

− xx

h) x3 + 2x2 – x – 2= ( ) ( ) ( )2·1·1 +−+ xxx

i) 2x4 – 6x3 – 6x2= ( )33·2 22 −− xxx

j) x3 – 2x2 – 5x + 6= ( ) ( ) ( )3·2·1 −+− xxx

k) 2x4 – 5x3 – x2 + 6x= ( ) ( )

−−+

2

3·2·1· xxxx

l) x4 – 3x3 – 19x2 + 27x + 90= ( ) ( ) ( ) ( )5·3·3·2 −−++ xxxx

m) x5 – x4 – x3 – x2 – 2x= ( ) ( ) ( )1·2·1· 2 +−+ xxxx

a. ( )( )( )( )3322

3613 24

+−+−=+−

xxxx

xxb. ( )( )55

253

−+=−xxx

xx

c. ( )( )( )4322

482822 23

−++−=++−−

xxx

xxxd. ( ) 3

23

3

27279

+

=+++

x

xxx

e. ( )( )( )732

428 23

++−=−++

xxx

xxx

f.

+

−

=−

2

5

2

54

254 3

xxx

xx