1. 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

2. SACAR FACTOR COMUN
36x4
- 48x6
- 72x3
+ 60x5
= 12x3
. (3x - 4x3
- 6 + 5x2
)
9x2
ab - 3xa2
b3
+ x2
az = 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 = ( )2
5·3 +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

3. 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
xx
b.
( )( )55
253
−+
=−
xxx
xx
c.
( )( )( )4322
482822 23
−++−
=++−−
xxx
xxx
d.
( )3
23
3
27279
+
=+++
x
xxx
e.
( )( )( )732
428 23
++−
=−++
xxx
xxx
f.






+





−
=−
2
5
2
5
4
254 3
xxx
xx