This document provides formulas for expanding binomial squares and cubes as well as formulas for difference and sum of cubes. It then provides 10 practice problems applying these formulas, such as finding expressions given information about variables, simplifying expressions, and expanding and reducing binomial expressions.

1. Prof. Javier Velásquez Espinoza
6º Primaria

2. Cuadrado del Binomio
(a + b) = a + 2ab + b
2
2
(a − b) = a − 2ab + b
2
2
2
2

3. Cubo del Binomio
(a + b) = a + 3a b + 3ab + b
3
3
2
2
3
(a − b) = a − 3a b + 3ab − b
3
3
2
2
3

4. Diferencia y Suma de Cubos
a3 – b3 = (a – b) (a2 + ab + b2)
a + b = (a + b) (a – ab + b )
3
3
2
2

5. 1.-Si: a + b = 2 y ab = 1,
hallar a2 + b2
2.-Sabiendo que:
(x + 1)2 =3, Calcular x2 + 2x – 2
3.-Si a + b = 4 y ab = 3,
hallar a3 + b3
4.-Si: a – b = 2 y ab = 15, Hallar a 3 – b3

6. 5.-Sabiendo que: (x + 2)2 = 36,
hallar x2 + 4x – 2
6.-Si: x + y = 5 y x . y = 6,
Hallar x2 + y2
7.-Reducir
(x + 1) (x – 1) + (x + 2)x + (x + 3) (x + 1) – x 2

7. 8.-Simplificar:
N =
(x
+ 4 ) ( x + 5) − 20
x 2 + 9x
9.-Si (a + b) = 6 y ab = 8,
hallar a3 + b3
10.-Reducir:
P = (x + 4) (x + 2) – 6x – 8