Types of Algebraic Expressions EXERCISE 5
1. Simplify the following: (a) x
__ 2 + 1
(b) x __
(c) x __
5 7
__ 3
3 − 1 __
2 + x __
(d) 5x ___
4 − 2x ___
3
(e) x − x __
3
__ 5 × 17
___ 2
(f) x __
4 − 2x ___
(g) 2x ___
3 + 1
3 − x + 1 _____
2
(h) x + 1 _____
3 3
+ x + 4 _____
5
(i) 2x + 1 ______
(j) x − 1 _____
2. Simplify the following: (a) x
(b) − 2 __
(c) x __
3 × x __
2
3 × 2 ___
3x
(d) 3 ___
2x × x __
6
(e) − 5 ___
7x × 14x ____
35
(f) x __
5 × x __
3
(g) 2x ___
7 × 5x ___
3
(h) − 3x ___
(i) 4x ___
5 × − 7x ___
27
11 × 121x _____
16
(j) x + 1 _____
5
× x __
3
+ 5x + 1 ______
12
4 − 2x + 1 ______
6 (k)
_______ 4 −
3(x + 2)
(l) 1 __
x + 1 (m) 3 (n) (o)
(k) x + 1 _____
3 7
_____ x + 1
_____ x + 2 + 2
_______ 2(x + 1) +
3
_____ x + 2 − 2
5
× x − 1 _____
7
(l) 2x + 1 ______
(m) 3x + 2 ______
12
(o) 8x + 4 ______
7
× 14 _____
x − 1 × 24
(n) −5x + 7 _______
_______ 12x + 8
6 − 4x × 9 − 6x ________
21 − 15x
× 21x _______
16x + 8
_____ x + 3
_______ 3(x + 2)
2
_____ x − 3
______ 2
3x + 1 (p) (q) (r)
______ 2x − 3 − 1
5
_______ 5(x − 1) − 1
3 x
_____ x + 1 + x
(s) x + 2 _____
_____ x − 1
x − 2 − x − 2 _____
x + 2
(t) 3x − 1 ______
(p) x + 1 _____
2
3x + 1 − 3x + 1 ______
3x − 1
x − 2 × 5x − 10 _______
3x + 3
(q) 2 x + 2 ______
× 6 x − 10 _______
(r) 7x − 14 _______
(s) x − 1 ______
(t) 1 − x _____
5 (x + 2) × 3
______ (x − 2)
5x + 7 × −25x − 35 _________
3 − 3x
× 5x + 10 _______
x − 1 4.3 Exponential expressions (powers)
You already know that 23 = 2 × 2 × 2 and y 4 = y × y × y × y, but what do 2
__ 3
1 , 3
__ 5
2
, 3 − 1 __
2 mean? These are all exponential expressions.
An exponential expression is an expression of the form a p, p ∈. KEY TERM
ACTIVITY ACTION CTION Evaluating powers
OBJECTIVE To simplify powers by multiplying brackets
Y 17
a is called the base of the expression. p is called the power or the index or the exponent of the expression.
(3)2 = 3 × 3 = 9 (−2)3 = (−2) × (−2) × (−2) = −8 y4
( y __
2 ) = 4
( − 3 __
( 2 1 __
__ 2 ×
y
2 ) = 3
2 ) = 2
__ 2 ×
y
( − 3 __
( 5 __
2 ) = 2
__ 2 ×
y 2 ) ×
( 5 __
__ 2 =
y
( − 3 __
2 ) ×
___ 16
2 ) × 2
( 5 __
( − 3 __
2 4
) = − 27 ___
8
) = 25 ___
77 5 − 3x × 1
_____ x + 1
__ x
_______ (2x + 3)
4
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