Simplification and Approximation Tricks | Solve Questions in 10 Seconds

Dear students, to solve the large expression type approximation problems quickly you must remember few algebraic formulas which we have enlisted below.
Important formula of algebra Which are Used to Solve Simplification and Approximation Problems Quickly:
1. (a+b)^2 = a^2+b^2+2ab
2. (a-b)^2 = a^2+b^2-2ab
3. (a+b)^2 = (a-b)^2+4ab
4. (a-b)^2 = (a+b)^2-4ab
5. (a+b)^3 = a^3+b^3+3ab(a+b)
6. (a-b)^3 = a^3-b^3-3ab(a-b)
7. a^3+b^3 = (a+b)(a^2-ab+b^2)
8. a^3-b^3 = (a-b)(a^2+ab+b^2)
9. (a+b+c)^2 = a^2+b^2+c^2+2(ab+bc+ca)
10. a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)
11. If a+b+c=0 then a^3+b^3+c^3=3abc
Shortcuts Solution of the Questions given below:

Q1. (299.12 + 312.01)^2 / (299.12 + 312.01)

Shortcut Solution: Apply 1st formula:

(299.12 + 312.01)^2 / (299.12 + 312.01)
=(299.12 + 312.01)((299.12 + 312.01)) / (299.12 + 312.01)
=(299.12 + 312.01)
=299+312
=611
Q2. (998.10)^3 + (888.10 )^3 / (998.10)^2+(888.10)^2-(998.10*888.10)

Shortcut Solution: Apply 7th formula:

(998.10)^3 + (888.10 )^3 / (998.10)^2+(888.10)^2-998.10*888.10
=(998.10+888.10 )(998.10)^2+(888.10)^2-998.10*888.10) / (998.10)^2+(888.10)^2-(998.10*888.10)
=998.10+888.10
=998+888
=1886

Q3. (1.33 - 1.22)^2 / (1.33^2 - 1.33*1.22 + 1.22^2)

Shortcut Solution: Apply 2nd formula:

(1.33 - 1.22)^2 / (1.33^2 - 1.33*1.22 + 1.22^2)

= (1.33^2 - 1.33*1.22 + 1.22^2) / (1.33^2 - 1.33*1.22 + 1.22^2)
=1

Q4. (11.11)^3+(22.22)^3+(33.33)^3-3*11.11*22.22*33.33 / (11.11)^2+(22.22)^2+(33.33)^2-11.11*22.22-22.22*33.33-33.33*11.11

Shortcut Solution: Apply 10th formula:

(11.11)^3+(22.22)^3+(33.33)^3-3*11.11*22.22*33.33 / (11.11)^2+(22.22)^2+(33.33)^2-11.11*22.22-22.22*33.33-33.33*11.11
=(11.11+22.22+33.33)(11.11)^2+(22.22)^2+(33.33)^2-11.11*22.22-22.22*33.33-33.33*11.11 / (11.11)^2+(22.22)^2+(33.33)^2-11.11*22.22-22.22*33.33-33.33*11.11
= (11.11+22.22+33.33)
=11+22+33
=66

Q5. (5.14)^3 - (3.12)^3 / (5.14)^2+5.14*3.12+(3.12)^2

Shortcut Solution: Apply 8th formula:

(5.14)^3 - (3.12)^3 / (5.14)^2+5.14*3.12+(3.12)^2
= (5.14 - 3.12)(5.14)^2+5.14*3.12+(3.12)^2 / (5.14)^2+5.14*3.12+(3.12)^2
=5.14-3.12
=5-3
=2

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