The document provides formulas for squaring binomial expressions and factoring polynomials. It lists the formulas for squaring terms of the form (a ± b)2 and expressions involving addition or subtraction of terms. It also gives examples of factoring polynomials into their prime factors and performing arithmetic operations on polynomials.

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