### Common Errors in Secondary Mathematics

Common Errors Committed  by the  Students  in Secondary Mathematics   Errors  that students often make in doing secondary mathematics  during their practice and during the examinations  and their remedial measures are well explained here stp by step.  Some Common Errors in Mathematics

### 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.

1. Very useful for me

2. Thanks for this