SIMPLIFYING EXPRESSIONS

Simplifying the following
x y x y
1. 2(5 ) 3(3 )
x x
2. 2(3 1) ( 2)
y
y
3. 2 3( 1)
6. Expand and simplify
(2x5)(3x
4)
7.
2 2
9x
y
9x
3y
m
m
4. 3 2( 1)
5. 3(3x 1) (6x
3)
8.
2x3 x2
5 3

9.
3 2 3
2 m
16.
2 3
x1 x
1
10. Express as a single
fraction
3
2
p
p
q
17. Express as a single
fraction
4
3
x 1 2
x 1
11.
5 7 1
y y 2
18.
2x
6
x3 3
x
12.
2 a 2
3 2a
19.
3 2
3t1 2t1
13.
3 2
y y 2
20.
b 2
b5 b3
14.
2 3
a
3 a
21.
1 2
p2 4p3
15. Write as a single
fraction in its
simplest form
3 4
x x 1
22.
4 5 x
x 2x
2

Word Problems
23. In a multiple choice test of 30 items, each candidate is
given a bonus mark of 30. A candidate earns 3 marks for
each correct answer and loses 1 mark for each incorrect or
omitted answer.
Assuming that a candidate gets x correct answers, show that
the total number of marks received must be divisible by 4
24. ……..
i. Alice hat t tapes and Ben has 10 tapes more than Alice.
Express, in terms of t, the number of tapes Ben has.
ii. Alice gives Ben 14 of her tapes. Ben now has twice as
many tapes as Alice now has
Write an algebraic expression to represent the amount
each person now has
25. Adam, Imran, and Shakeel were playing a card game.
Adam scored x points. Imran scored 3 points fewer than
Adam. Shakeel scored twice as many points as Imran
Together they scored 39 points
i. Write down in terms of x an expression for the
number of points scored by Shakeel.
Write an equation which may be used to find the value of x.