Simplification, Definition, Formula, and Examples

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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:

1. The Organization advises on the simplification of trade Procedures.
2. 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 = 4³
x = 3

Q4. 450 ÷ 15 + 208 ÷ 8 – 16 = ?² – 41
A. 8
B. 9
C. 7
D. 6

450 ÷ 15 + 208 ÷ 8 – 16 = x² – 41
(450/15) + (208/8) – 16 + 41 = x²
30 + 26 – 16 + 41 = x²
x² = 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
8² + 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
x² = (7 × 16 × 307)/2149
x² = 16
x = 4

Q.9 2116^1/2  – 2³ % of 2700 + 180 = ?
A. 11
B. 10
C. 12
D. 9

2116^1/2  – 2³ % 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. 3⁴ ÷ (3 * 3²) + 12² ÷ (4 * 2) = ?
A. 21
B. 42
C. 62
D. 81

3⁴ ÷ (3 * 3²) + 12² ÷ (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. 4² × 5 + 40 × 11 = ? × 13
A. 20
B. 30
C. 50
D. 40

4² × 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

Read More :
Discount	Profit and Loss	Simple Interest
Simplification	LCM and HCF	Compound Interest

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