Simplification Questions, Formulas, Shortcuts and Practice Problems
Rule of Simplification
- In simplifying an expression, first of all vinculum or bar must be removed. For example: we know that -4-5 = -9 but, –\(\overline{4-5}\) = -(- 1) = 1
- After removing the bar, the brackets must be removed, strictly in the order (), {} and [].
- After removing the brackets, we must use the following operations strictly in the order given below, (a) of (b) division (c) multiplication (d) addition and (e) subtraction
Ex 1:
Solution:
Simplification Questions on Application of Algebra Formulas
2. (a + b)2 = a2 + b2 + 2ab
Ex 2: Simplify 0.46 x 0.46 + 0.54 x 0.54 + 0.92 x 0.54
Solution:
We have the expression
0.46 x 0.46 + 0.54 x 0.54 + 0.92 x 0.54 = (0.46)2 + (0.54)2 + 2. x 0.46 x 0.54
If we suppose a = 0.46 and b = 0.54, then
= a2 + b2 + 2ab = (a + b)2
= (0.46 + 0.54)2 = (1.00)2 = 1
∴ Answer = 1.
3. (a – b)2 = a2 +b2 – 2ab
Ex 3. simplify 1.66 × 1.66 + 0.66 × 0.66 – 1.32 × 1.66
Solution:
We have the expression
1.66 × 1.66 + 0.66 × 0.66 – 1.32 × 1.66
Now, applying the above formula,
= (1.66 – 0.66)2 = (1)2 = 1
∴ Answer = 1
4. (a + b)2 +(a- b)2 = 2 (a2 + b2)
Ex 4: Simplify the following
2[1.25 x 1.25 + 0.25 x 0.25]
Solution:
Applying the above formula, we have
2[(1.25)2 + (0.25)2 ] = (1.25 + 0.25)2 + (1.25 – 0.25)2
= (1.5)2+ (1)2
= 2.25 + 1 = 3.25
5. (a + b)2 – (a- b)2 = 4ab
Ex 5:
Solution:
Applying the above formula, we have a = 14.5, and b = 6.23
6. (a + b) (a – b) = a2 –b2
Ex 6:
Simplify (502 – 402) =? X 45
Solution:
Suppose a = 50 and b = 40
And required number = x
Applying the above formula,
∴ Required answer = 20.
7. (a + b)3 = a3 + + 3a2b + 3ab2 + b3 = a3 + b3 + 3ab (a + b)
Ex 7:
Simplify (0.6)3 + (0.4)3 + 3 x 0.6 x 0.4(0.6 + 0.4)
Solution:
The above expression can be written as
(0.6)3 + (0.4)3 + 3 x 0.6 x 0.4(0.6 + 0.4)
Now, we suppose 0.6 = a and 0.4 = b and applying the above formula, we have (0.6 + 0.4)3 = (1)3 = 1
8. (a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab (a-b)
Ex 8:
Simplify
Solution:
9. a3 +b3 = (a + b)(a2 – ab + b2)
Solution:
Here a = 0.5 and b = 0.4
∴ Required answer = 0.5 + 0.4 = 0.9
10. a3 – b3 = (a- b) (a2 +ab + b2)
Ex 10:
Solution:
Simplification Questions – Practice Problems
Simplification Practice Problems Answers
1. 4505
2. 2
3. 49
4. 10
5. 104
6. 108.45
7. 0.46
8. 315
9. \(13 \frac { 3 } { 10 }\)
10. \( \frac { 3 } { 7 }\)
11. 12
12. 2
13. \( \frac { 61 } { 11 }\)
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