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On the previous page, we had shared the information about **Simple Interest** and **Compound Interest**, so read that article as well.

Let us read and understand the information about Simplification, Definition, Formula, and Examples today.

## Definition of Simplification

the process of making something less complicated and therefore easier to do or understand, or the thing that results from this process:

- The Organization advises on the simplification of trade Procedures.
- This is a gross simplification of what actually happened.

**Fewer Examples :-**

- There are many simplifications in the new design.
- He is proposing massive simplification of the tax system.
- The group have welcomed the proposed simplifications.

## Simplification Formulas

Apart from the above sequence, various algebraic formulas are also used in the simplification of expressions.

**Important Identities of Simplification :**

Common Factor : c(a + b) = ca + cb

**Square of Binomial :**

- (a + b)² = a² + 2ab + b²
- (a – b)² = a² – 2ab + b²

Product of sum and difference of two terms : a² – b² = (a+b) (a-b)

**Other identities (sum and difference of cubes) :**

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

**Cube of Binomial :**

- (a + b)³ = a³ + 3a²b + 3ab² + b³
- (a – b)³ = a³ – 3a²b + 3ab² – b³

**Square of the polynomial :**

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

Multiplication of two binomials with a common term : (x + a )(x + b ) = x² + (a + b )x + ab

**Gauss’s identity :** a³ + b³ + c³ – 3abc = (a+b+c) (a² + b² + c² – ab -bc – ca)

**Legendre identity :**

- (a+b)² + (a-b)² = 2(a² + b²)
- (a+b)² – (a-b)² = 4ab)
- (a+b)4 – (a-b)4 = 8ab(a² + b²)

**Lagrange’s identity :**

- (a² + b²) (x² + y²) = (ax+by)² + (ay-bx)²
- (a² + b² + c²) (x² + y² + z²) = (ax+by+cz)² + (ay-bx)² + (az-cx)² + (bz-cy )²

## Simplification Examples

**Q1. 30% × 580 + 60% of 700 =?^{2} + √4225**

**A**. 21

**B**. 23

**C**. 25

**D**. 27

**30% of 580 + 60% of 700 = ? ^{2} + √4225**

30/100 × 580 + 60/100 × 700 = ?

^{2}+ √4225

58 × 3 + 70 × 6 = ?

^{2}+ 65

174 + 420 = ?

^{2}+ 65

594 = ?

^{2}+ 65

594 – 65 = ?

^{2}

529 = ?

^{2}

(23)

^{2}= ?

^{2}

? = 23 Answer.

**Q2. 70 % of 540 – 120 % of 350 = ? × 6****A**. -6**B**. -5**C**. -7**D**. -8

70 % of 540 – 120 % of 350 = ? × 6

70/100 × 540 – 120/100 × 350 = ? × 6

7 × 54 – 12 × 35 = ? × 6

378 – 420 = ? × 6

-42/6 = ?

? = -7

**Q3. 4 ^{?} × (225)^{1/2} = 248 ÷ 8 + 929**

**A**. 2

**B**. 4

**C**. 3

**D**. 5

4^{x} × (225)^{1/2} = 248 ÷ 8 + 929

4^{x} * 15 = (248/8) + 929

4^{x} = (31 + 929)/15

4^{x} = 64

4^{x} = 4^{3}

x = 3

**Q4. 450 ÷ 15 + 208 ÷ 8 – 16 = ? ^{2} – 41**

**A**. 8

**B**. 9

**C**. 7

**D**. 6

450 ÷ 15 + 208 ÷ 8 – 16 = x^{2} – 41

(450/15) + (208/8) – 16 + 41 = x^{2}

30 + 26 – 16 + 41 = x^{2}

x^{2} = 81

x = 9

**Q.5 (√8 x √8) ^{2} + (9)^{1/2} = (?)^{3} + 3**

**A**. 4

**B**. 2

**C**. 16

**D**. 5

(√8 x √8)^{2} + (9)^{1/2} = (?)^{3} + 3

8^{2} + 3 = (?)^{3} + 3

(?)^{3 }= 64

? = 4

**Q6. [{(150% of 44) – 11} % of 660] % of 25 = (?) % of 165****A**. 65**B**. 45**C**. 44**D**. 55

[{(150% of 44) – 11} % of 660] % of 25 = (?) % of 165

[{66 – 11} % of 660] % of 25 = x % of 165

[55 % of 660] % of 25 = x % of 165

363 % of 25 = x % of 165

? = 9075/165 = 55

**Q7. 40% of 525 + 25% of 340 = ? + 95****A**. 180**B**. 190**C**. 200**D**. 210**E**. 220

40% of 525 + 25% of 340 = ? + 95

210 + 85 =? + 95

? = 200

**Q8. ?/16 = 7/? × 1/2149 × 307****A**. 7**B**. 4**C**. 4.5**D**. 3

?/16 = 7/? × 1/2149 × 307

x^{2} = (7 × 16 × 307)/2149

x^{2} = 16

x = 4

**Q.9 2116 ^{1/2 } – 2^{3} % of 2700 + 180 = ?**

**A**. 11

**B**. 10

**C**. 12

**D**. 9

2116^{1/2 } – 2^{3} % of 2700 + 180 = ?

2116^{1/2} – 8/100 x 2700 + 180 =?

46 – 8 x 27 + 180 =?

46 – 216 + 180 =?

10 =?

**Q10. 4572 ÷ 12 * 14 – 222 =?****A**. 4590**B**. 5112**C**. 2567**D**. 3908

4572 ÷ 12 * 14 – 222 =?

=> 381 * 14 – 222 =?

=> 5112

**Q11. 3 ^{4} ÷ (3 * 3^{2}) + 12^{2} ÷ (4 * 2) = ?**

**A**. 21

**B**. 42

**C**. 62

**D**. 81

3^{4} ÷ (3 * 3^{2}) + 12^{2} ÷ (4 * 2) = ?

=> 3 + 18

=> 21

**Q12. (1/6) * 123 + (1/8) * 120 – ? = 33****A**. 1.5**B**. 2**C**. 2.5**D**. 3

(1/6) * 123 + (1/8) * 120 – ? = 33

=> 20.5 + 15 – ? = 33

=> 2.5

**Q13. 50% of ? = 45 + 25 * 6 ****A**. 200**B**. 250**C**. 390**D**. 420

50% of ? = 45 + 25 * 6

=> 50% of ? = 195

=> 390

**Q14. 55% of 800 + 33 x 4 – 396 ÷ 18 = (?)² – (13 x 2)****A**. 24**B**. 26**C**. 34**D**. 36

55% of 800 + 33 x 4 – 396 ÷ 18 = (?)² – (13 x 2)

440 + 132 – 22 + 26 = (?)²

550 + 26 = (?)²

(?) = √576

(?) = 24

**Q15. 325 × 16 ÷ 4 + 37 + 50 = ?****A**. 1300**B**. 1230**C**. 1340**D**. 1387

325 × 16 ÷ 4 + 37 + 50 = ?

325 × (16/4) + 37 + 50 = ?

325 × 4 + 87 = ?

1300 + 87 = ?

1387 = ?

**Q16. (175 × 15 ÷ 25 + 895) ÷ 5 = ?****A**. 300**B**. 200**C**. 1000**D**. 1250

(175 × 15 ÷ 25 + 895) ÷ 5 = ?

(175 × (15 ÷ 25) + 895)/5 = ?

(105 + 895)/5 = ?

1000/5 = ?

200 = ?

**Q17. 4 ^{2} × 5 + 40 × 11 = ? × 13**

**A**. 20

**B**. 30

**C**. 50

**D**. 40

4^{2} × 5 + 40 × 11 = ? × 13

80 + 440 = ? * 13

? = 40

**Q18. 60% of 240 + 20% of 280 = ?****A**. 180**B**. 200**C**. 220**D**. 240

60% of 240 + 20% of 280 = ?

144 + 56 = ?

200 = ?

**Q19. 1560 ÷ 12 – 4004 ÷ 13 = ? ^{2} – 322**

**A**. 12

**B**. 16

**C**. 18

**D**. 10

1560 ÷ 12 – 4004 ÷ 13 = ?^{2} – 322

130 – 308 = ?^{2} – 322

12 = ?

**Q20. √289 × 25 – 17 × 14 = ?****A**. 165**B**. 187**C**. 163**D**. 183

√289 × 25 – 17 × 14 = ?

17 × (25 – 14) = ?

? = 187

## FAQ

**Q.1 What do you mean by simplification?**

**Ans.** the process of making something less complicated and therefore easier to do or understand, or the thing that results from this process

**Q.2 What is the basic of simplification?**

**Ans.** determining the solution by reducing or simplifying it from the complex calculation.

**Q.3 Why is simplification important?**

**Ans.** makes internal operations less complex and more efficient.

**Q.4 What is the full form of Bodmas?**

**Ans.** Bracket, Of, Division, Multiplication, Addition, and Subtraction.

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