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From the results of Exploration Activity 1, it is found that
3
2
a × a = a a × a × a = a a × a × a × ... × a = a n Power of n

Repeated Repeated Repeated
multiplication multiplication multiplication
of a by 2 times of a by 3 times of a by n times

Hence, generalisations regarding the repeated multiplication of algebraic expressions are
recognised as follows.
(a + b) × (a + b) = (a + b) 2
(a + b) × (a + b) × (a + b) = (a + b) 3
(a + b) × (a + b) × (a + b) × (a + b) = (a + b) 4
In general, CHAPTER
n
(a + b) × (a + b) × (a + b) × ... × (a + b) = (a + b) Power of n
5
Repeated multiplication of the algebraic
expression (a + b) by n times

9

Simplify each of the following:
(a) m × m × m × m (b) (x + 7) × (x + 7)
(c) (p – 3q) × (p – 3q) × (p – 3q)

(a) m × m × m × m = m (b) (x + 7) × (x + 7) = (x + 7) 2
4

Multiplication is repeated 4 times Multiplication is repeated 2 times
(c) (p – 3q) × (p – 3q) × (p – 3q) = (p – 3q)
3

Multiplication is repeated 3 times

10
Write each of the following in the form of repeated multiplication:
2
(a) (x + 4y) (b) (9p – q)
3

3
(a) (x + 4y) = (x + 4y)(x + 4y) (b) (9p – q) = (9p – q)(9p – q)(9p – q)
2
Self Practice 5.2b

1. Simplify each of the following:
(a) pq × pq × pq (b) (6a – 1) × (6a – 1)
(c) (8x + 3y) × (8x + 3y) × (8x + 3y)
2. Write each of the following in the form of repeated multiplication:
2
4
(a) (2 + 7x) (b) (h – 4k) (c) (5p + q)
3
115
Algebraic Expressions

05 TB Math F1.indd 115 11/10/16 12:13 PM