When the express the given expression in the simplest form, then it is known as simplification. In order to simplify an expression, we use the operations in the following order, which is known as BODMAS rule.

- B - Bracket
- O - Of
- D - Division
- M - Multiplication
- A - Addition
- S - Substraction

- Vi - Viniculum of Bar '-'
- Ci - Circular Bracket ()
- Cu - Curly Bracket {}
- Sq - Square Bracket []

IMPORTANT FORMULA

1. a÷b÷c=a×1b×1c

2. abc+ def - ghi = (a+d-g)+bc+ef-hi

3. (a+b)2-(a-b)2=4ab

4. x+x+x+....∞=n+1, if x=n(n+1)

5. m of n%=m×n100

6. a-m=1am

7. am+1=am.a

8. am×a-n=am-n

9. am-1=am×1a, amn×nm=a, ax=1, then x=0

IMPORTANT FORMULA

1. bc+ec=b+ec

2. bc+ef=b×f+e×cc×f

3. ab÷cd=ab×dc

4. a×bcd=a×b+a×cd

5. abc+dec=(a+d)+b+ec

6. abc+def=(a+d)+b×f+c×ec×f

7. abc=a×cb

8. ab÷bc÷ce=ab×cb×ed

This is an important part of simplification. In which some difficult problem are solved by using the algebraic formula

1. (a+b)2=a2+2ab+b2=(a-b)2+4ab

2. (a-b)2=a2-2ab+b2=(a+b)2-4ab

3. a2+b2=(a+b)2+(a-b)22

4. a2-b2=(a+b)(a-b)

5. (a+b)3=a3+b3+3ab(a+b)

6. (a-b)3=a3-b3-3ab(a-b)

7. a3+b3=(a+b)(a2-ab+b2)

8. a3-b3=(a-b)(a2+ab+b2)

9. ab=(a+b)2-(a-b)24

10. (a+b+c)2=a2+b2+c2+2(ab+bc+ca)

11. a3+b3+c3-3abc=(a+b+c)(a2+b2+c2-ab-bc-ca)

12. if a+b+c=0, then a3+b3+c3=3abc

Per Cent is made of two words per and cent. Meaning of per and cent is "per hundred". Sign of per cent is '%'. Meaning of 35% is 35100 1.e., 35 parts out of 100 parts.

1. n% of m=m×n100

2. Number +A% of Number=Number×100+A100

3.Number - A% of Number=Number×100-A100

4. If the value of number is first increased by A% and later decreased by A% then the next change is always a decrease which is equel to A2100%

5. If an object price in increased or decreased by A% and the other factor is increased or decreased by B%, then the net effect is given by

Net effect=±A±B+±A±B100%

2%=150 | 4%=125 | 8%=225 | 16%=425 | 64%=1625 |

5%=120 | 10%=110 | 20%=15 | 40%=25 | 70%=710 |

25%=14 | 50%=12 | 75%=34 | 250%=52 | 110%=1110 |

614%=116 | 1212%=18 | 1623%=16 | 3313%=13 | 6623%=23 |

Square, when any number is multiplied by itself, then the produce is known as square of the number.

e.g., Square of 5=52=5×5=25

Square Root, Square may be define the number whose square is equal to given number. In other words, square root of a given number is the number when multiplied by itself, gives the product equal to the given number.

e.g., Square root of 16=16=4

Cube, cube of a number is the triple product obtained on multiplying the number by itself.

e.g., Cube of 5=53=5×5×5=125

Cube Root, cube root of a number is the number whose cube is the given number.

e.g., Cube root of 216=2163=6×6×63=6

1. ann=a

2. anm=amn

3. abn=an×bn

4. anm=amn

5. abn=anbn

6. a×b×c=abc

1. am×an=am+n

2. am÷an=am-n

3. (am)n=amn

4. abm=am×bm

5. abm=ambm

6. a0=1