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Ejercicios de identidades notables y polinomios
A) Desarrolla las siguientes identidades notables:
1.
(x+~r =
2. (2x
5. (1+2y)l =
+S}2 =
6. (2x-3y}2 =
+ l3x l 2y) = 10. (~-%Xr =
9. (3x 2 2y
13. ( x
+~).(x ~) =
17.
(Xl +6xlx2 6x)=
21.
(2;
_;y =
3. (X2 +3xJ~
=
4. (6- X)2 =
. (~+~X)(~-~X)= 43 43
7
11. (SX-
1~ Xr = y3)2
(3; +ir =
15. ~2
_
18.
(Xl 2xy =
19. (X2
-~yr =
22.
(3- 2Z)3 =
23.
jr =
12. (x 2 _S)2 =
=
14.
8. (x-
16. (S+ 4x)(S 4x) =
(3- 2)3 =
20.
(%+~r =
24.
(3- 2y}2 - (3+ 2y}l =
B) Factoriza los siguientes polinomios utilizando las identidades notables:
1.
xl + 10x+25 =
5. 49- x2
=
2. 4x2 + 12x+9 =
3. 4-4x2 +x4 =
4. 9x2 -4 =
6. 9-4x2 =
7. x 4 -1 =
x6- x 2 8. 4
=
C) Desarrolla estas operaciones, aplicando las identidades notables y reduciendo los términos semejantes: " i
1. (x+
+
2)2 - (x- 3)(x+ 3) =
2. {2x 1}2 - (2x
3. (3x - Sr;¡ + (3x+ S)2 =
4. SX(X2 - 2x i
5. (X2
-1)(x2 +1)- x
4
=
7. (x-2)(2x-4)+2x(4-x)
+3}(x 2) =
+3)- (x + 3)2 =
6. (x+S)(-S+x)+(X-S)2 =
8.
+
(x- 3)2x (7 2x)(x-2)=
i
Página 2 de 2
3x(x- 2}2 -l2(x - X2)=
9. 2x(2x-l}:l 2x(2x+ 1}2 =
10.
11. (2x 2+ 3x)(2x 2 - 3x)- X2 (2x- 3}2 =
12. -4xl(x-l}2 -8(X+x2)j=
13. (3x -1)x 2+ 3x(x 2 +4)- 6(2x + x3 ) =
14.
(x- 3)x + 2(x- 2x 2)+ 3(X2 + x)=
15. (x-1)3 - 2x+ (1- X)(X2 + x+ 1)=
16.
(x 2-2)(x 2+2)-(2-x2 =
18.
x:l + (X-lr 4 2
20.
(2x +3}:l +(2x - 3}2
17.
(X2 -l)l(x:l +1)-(1-x2)J=
19. (X;3r _ X2 -!X+9 = 21. (2x+3)2 -(2x-3}2
23.
=
(~X-%)(~X+%)-(~X-%r =
f
=
22. a2 (a- b)2 +(a +b)(a- b)+ 2a(a- b):::
24. (¡X-2)(%X+2)-(¡X+2r =