Algebraic Identities Of Polynomials

Algebraic Identities Of Polynomials

Algebraic identities, for classes 7th, 8th, 9th, 10th, 11th, 12th, Algebraic identities required for polynomials, square table, cubic table, method of making algebraic identities, pascal triangle.

In order the start solving the mathematical concepts with interest, students should have some knowledge of basic concepts. Some previous topics are also compulsory for the students because these concepts helps the students in understanding the next level. So here in this post we learn the following topics.

INDEX
1	Square Table
2	Cubic Table
3	Algebraic Identities

SQUARE TABLE

For fast calculation it is compulsory for the students to learn the square table. Square table help the students, while solving the problems and it also increase the interest of the students. 

SQUARE TABLE
NUMBER	SQUARE		NUMBER	SQUARE
12	1		212	441
22	4		222	484
32	9		232	529
42	16		242	576
52	25		252	625
62	36		262	676
72	49		272	729
82	64		282	784
92	81		292	841
102	100		302	900
112	121		312	961
122	144		352	1225
132	169		402	1600
142	196		452	2025
152	225		502	2500
162	256		552	3025
172	289		602	3600
182	324		652	4225
192	361		702	4900
202	400		752	5625

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CUBIC TABLE

For fast calculation it is compulsory for the students to learn the cubic table. Cubic table helps the students, while solving the problems and it also increase the interest of the students. 

CUBIC    TABLE
NUMBER	CUBE		NUMBER	CUBE
13	1		113	1331
23	8		123	1728
33	27		133	2197
43	64		143	2744
53	125		153	3375
63	216		163	4096
73	343		173	4913
83	512		183	5832
93	729		193	6859
103	1000		203	8000

Algebraic Identities

Algebraic identities are very useful at every level for solving the algebraic problems. If you want to be perfect in algebra you should have the knowledge of Algebraic Identities. 

Up to 10th standard students should learn first 14 Algebraic Identities.

Last five Algebraic Identities are specially for the students 11th and 12th .

1	(a + b)2         = a2 + b2 + 2ab
2	(a - b)2          = a2 + b2 – 2ab
3	(a + b)(a - b)  = a2 – b2
4	(x + a)(x + b)  = x2 + (a + b)x + ab
5	(a + b + c)2   = a2 + b2 + c2 + 2ab + 2bc + 2ca
6	(a + b)3     = a3 + b3 + 3ab(a + b)  or  a3 + b3 + 3a2b + 3ab2
7	(a - b)3    = a3 - b3 - 3ab(a - b)  or  a3 - b3  - 3a2b + 3ab2
8	a3 + b3   = (a + b)(a2 + b2 - ab)
9	a3 - b3     = (a - b)(a2 + b2 + ab)
10	a3 + b3 + c3 - 3abc = (a + b + c)(a2+ b2 + c2 –  ab – bc - ca)  If  a + b + c = 0 then a3+b3+c3 = 3abc
Some Special Identities
11	a2  + b2  = (a + b)2 - 2ab
12	a2  + b2   = (a - b)2  + 2ab
13	a3 + b3  = (a + b)3- 3ab(a + b)
14	a3 - b3    = (a - b)3 + 3ab(a - b)

Next Algebraic identities are useful for the students after 10th standard. 

1	This Algebraic Identity can be used while finding the square root of a complex number in chapter 5 class 11 (a2 + b2)2  =   (a2 - b2)2  + 4a2b2
2	These Algebraic Identities(2 to 5) can be derived with the help of Binomial Expansion Chapter 8 class 11 (a + b)4  = a4 + 4a3b + 6a2b2 + 4ab3 +  b4
3	(a - b)4  = a4 - 4a3b + 6a2b2 - 4ab3 + b4
4	(a + b)5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5
5	(a - b)5 = a5  - 5a4b + 10a3b2  - 10a2b3 + 5ab4  - b5

We can find the algebraic identities with the higher order by using Binomial Expansion.

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