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Algebraic Identities Of Polynomials
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INDEX 

1 
Square Table 
2 
Cubic Table 
3 
Algebraic Identities 
SQUARE TABLE
SQUARE TABLE 

NUMBER 
SQUARE 
NUMBER 
SQUARE 

1^{2} 
1 
21^{2} 
441 

2^{2} 
4 
22^{2} 
484 

3^{2} 
9 
23^{2} 
529 

4^{2} 
16 
24^{2} 
576 

5^{2} 
25 
25^{2} 
625 

6^{2} 
36 
26^{2} 
676 

7^{2} 
49 
27^{2} 
729 

8^{2} 
64 
28^{2} 
784 

9^{2} 
81 
29^{2} 
841 

10^{2} 
100 
30^{2} 
900 

11^{2} 
121 
31^{2} 
961 

12^{2} 
144 
35^{2} 
1225 

13^{2} 
169 
40^{2} 
1600 

14^{2} 
196 
45^{2} 
2025 

15^{2} 
225 
50^{2} 
2500 

16^{2} 
256 
55^{2} 
3025 

17^{2} 
289 
60^{2} 
3600 

18^{2} 
324 
65^{2} 
4225 

19^{2} 
361 
70^{2} 
4900 

20^{2} 
400 
75^{2} 
5625 
CUBIC TABLE
CUBIC
TABLE 

NUMBER 
CUBE 
NUMBER 
CUBE 

1^{3} 
1 
11^{3} 
1331 

2^{3} 
8 
12^{3} 
1728 

3^{3} 
27 
13^{3} 
2197 

4^{3} 
64 
14^{3} 
2744 

5^{3} 
125 
15^{3} 
3375 

6^{3} 
216 
16^{3} 
4096 

7^{3} 
343 
17^{3} 
4913 

8^{3} 
512 
18^{3} 
5832 

9^{3} 
729 
19^{3} 
6859 

10^{3} 
1000 
20^{3} 
8000 
Algebraic Identities
1 
(a + b)^{2}
= a^{2} + b^{2} + 2ab 
2 
(a  b)^{2}
= a^{2} + b^{2} –
2ab 
3 
(a + b)(a  b) = a^{2} –
b^{2} 
4 
(x + a)(x + b) = x^{2} +
(a + b)x + ab 
5 
(a + b + c)^{2 } =
a^{2} + b^{2} + c^{2} + 2ab + 2bc +
2ca 
6 
(a + b)^{3} = a^{3 }+
b^{3 }+ 3ab(a + b) or a^{3 }+
b^{3 }+ 3a^{2}b + 3ab^{2} 
7 
(a  b)^{3 }=
a^{3 } b^{3 } 3ab(a  b) or a^{3 }
b^{3 }  3a^{2}b + 3ab^{2} 
8 
a^{3 }+ b^{3} = (a + b)(a^{2 }+ b^{2 }
ab) 
9 
a^{3 } b^{3
}= (a  b)(a^{2 }+ b^{2 }+
ab) 
10 
a^{3 }+ b^{3 }+ c^{3 }
3abc = (a + b + c)(a^{2}+ b^{2 }+ c^{2 }– ab – bc 
ca) If a + b +
c = 0 then a^{3}+b^{3}+c^{3 }= 3abc 
Some Special
Identities 

11 
a^{2 }+
b^{2} = (a + b)^{2 } 2ab 
12 
a^{2 } +
b^{2} = (a  b)^{2 }+ 2ab 
13 
a^{3 }+ b^{3} =
(a + b)^{3} 3ab(a + b) 
14 
a^{3 } b^{3 } =
(a  b)^{3 }+ 3ab(a  b) 
1 
This Algebraic Identity can be used while finding the square root of a complex number in chapter 5 class 11 (a^{2} + b^{2})^{2}
= (a^{2 } b^{2})^{2} +
4a^{2}b^{2} 
2 
These Algebraic Identities(2 to 5) can be derived with the help of Binomial Expansion Chapter 8 class 11 (a + b)^{4 } =
a^{4 }+ 4a^{3}b + 6a^{2}b^{2 }+ 4ab^{3 }+ b^{4} 
3 
(a  b)^{4 } =
a^{4 } 4a^{3}b + 6a^{2}b^{2 } 4ab^{3 }+ b^{4} 
4 
(a + b)^{5} = a^{5 }+ 5a^{4}b + 10a^{3}b^{2 }+ 10a^{2}b^{3 }+ 5ab^{4 }+ b^{5} 
5 
(a  b)^{5} = a^{5 }  5a^{4}b + 10a^{3}b^{2 }  10a^{2}b^{3 }+ 5ab^{4 }  b^{5} 
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