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Let l = 12 m and b = 8 m, therefore,
The perimeter of the rectangle = 2 × (l + b) units
= 2 × (12 + 8) m [Q l = 12 m and b = 8 m]
= (2 × 20) m = 40 m

We can conclude from the above examples that to evaluate or find the value of an algebraic
expression, we need to know the numerical values of all the variables involving in it.

Thus, the process of replacing variables by their numerical values to obtain an arithmetic
expression is called substitution.

Maths Talk
Look around you to find the different rectangular shaped objects, measure their lengths and breadths and find
their perimeters by substituting those measurements in the expression 2(l + b) units. Is there any another way
to find the perimeters of different objects without using the above rule. Discuss.

Example 16: Find the values of the following expressions for x = 2.
(a) 2x – 5 (b) 4 + 3x
2
3
(c) x – 5 (d) x – 10x + 6
Solution: (a) Putting x = 2, 2x – 5 = 2 × 2 – 5 = 4 – 5 = –1
(b) Putting x = 2, 4 + 3x = 4 + 3 × 2 = 4 + 6 = 10

3
(c) Putting x = 2, x – 5 = 2 – 5 = 8 – 5 = 3
3
(d) Putting x = 2, x – 10x + 6 = 2 – 10 × 2 + 6 = 4 – 20 + 6 = –10
2
2
3
2
3
2
Example 17: Evaluate: a + 3a b + 3ab + b , if a = 1 and b = –1.
Solution: Substituting a = 1 and b = –1 in the given expression, we get
2
2
2
2
3
3
a + 3a b + 3ab + b = 1 + 3 × (1) × (–1) + 3 × (1) × (–1) + (–1) 3
3
= 1 + 3 × 1 × (–1) + 3 × (1) × 1 + (–1) [Q (–1) = 1 and (–1) = –1]
3
2
= 1 – 3 + 3 – 1 = 0
Practice Time 5E
1. Evaluate the following expressions by substituting the given values.
1
(a) 3p – 7, if p = –3 (b) 4m + 2 , if m = 2
1
(c) 3a – 2ab – 7, if a = – , b = 1 (d) 2xy – 2yz + xz, if x = –1, y = 1, z = –2
2 (
2
(e) t + t – 1, if t = 3 (f) nn − ) 1 , if n = 4
2
2. If x = 3, y = –2 and z = –1, find the values of the following expressions.

(a) x – y 2 (b) x – y – z 2 (c) xy + yz + zx (d) (x + y + z) 3
2
2
2
+
+
3
2
2
3
(e) x – 3x y + 3xy – y (f) xy yz zx (g) 4(2x – 1) + 3y + 11
xyz
117 Introduction to Algebra