1. ALGEBRAIC EXPRESSION II
CHAPTER 3

2. 3.3A . ALGEBRAIC EXPRESSIONS FOR GIVEN
SITUATIONS USING LETTERS.
Example :
Write an algebraic expression for each of
the following statements.
(a) Add 3 to p
(b) Subtract 2 from the product of 3 and x
(c) Divide the sum of m and n by 5
(d) Multiply 7 to half of t
p + 3 3x – 2
m + n
5
7t
2

3. example
Elaine bought 4 boxes of cakes from a
bakery. Each box contained x slices of
cakes. If Elaine ate y slices of the cakes,
find the number of cakes left.
Solution :
Total numbers of cakes = 4 x x
= 4x
Numbers of cakes left = 4x - y

4. 3.3B Recognising Algebraic Expression in
Two or more unknown
Example :
State the number of unknown in each of the
following algebraic expressions.
(a) 2a + 2b (b) 100 – 2pqr (c) hjk + 8p – 19q
Solution :
• 2a + 2b has two unknown : a and b
• 100 – 2pqr has three unknown : p, q and r
• hjk + 8p – 19q has five unknown : h, j, k, p and q

5. 3.3C Determining the Number of
terms in an Algebraic Expression
1. An algebraic expression can have only
one term
example: 8pq is an algebraic expression
with one term
2. A number can be consider a term.
example : 10rst -3 is an algebraic
expression with two terms

6. Determine the number of terms in each of
the following algebraic expressions
(a) 9m2n
(b) 2x2 – ½ yz + 11
(c) 4rs - 6st
5
Solution :
(a) 9m2n has one term
: 9m2n
(b) 2x2 – ½ yz + 11 has
three terms
: 2x2, ½ yz, and 11
(c) 4rs - 6st has two terms
5
:4rs and 6 st
5

7. 3.3D Simpliying Algebraic Expressions by
collecting Like Terms
When simpliying an algebraic
expression, only like terms
can be added or subtracted.

8. Simplify the following expressions
(a) 2ab + b + 5ab
Solution :
2ab + b + 5ab = 2ab + 5ab + b
= 7ab + b

9. Simplify the following expressions
(b) 2a2 + 3b + a2 + b
Solution :
2a2 + 3b + a2 + b = 2a2 + a2 + 3b + b
= 3a2 + 4b

10. Simpliying the following expressions
(c) 3mn – 10pq + 2mn - 4pq
Solution :
3mn – 10pq + 2mn - 4pq
= 3mn + 2mn – 10pq – 4pq
= 5mn – 14pq

11. 3.3E Evaluating an Expression
1. To evaluate an algebraic expression is to
find the value of the expression.
2 We can evaluate an algebraic expression
by subtituting numbers for letters
(replace letters with the given numbers)

12. Example :
Evaluate 2x + 5y when x = 4 and y = 2
Solution :
2x + 5y
= 2 (4) + 5 (2)
= 8 + 10
= 18

13. Example :
Evaluate 3c + 5 if c = 5 and d = 1
4d
Solution :
3c + 5 = 3 (5) + 5
4 d 4 (1)
= 15 + 5
4
= 20
4
= 5

14. Evaluate the following given p = 2
q = 4, r = 6, and
(a) p + 2q + 3r

15. Evaluate the following given p = 2
q = 4, r = 6, and
(b) 3p(p + q + r)

16. Evaluate the following given p = 2
q = 4, r = 6, and
(c) 2(p – q) + 3(s – r)

17. Evaluate the following given p = 2
q = 4, r = 6, and
(d) 3r – 2p(p + s)

18. Evaluate the following given p = 2
q = 4, r = 6, and
(e) p2 + 2pq + q2

19. Evaluate the following given p = 2
q = 4, r = 6, and
(f) ½ p2 (q + r)

20. Evaluate the following given p = 2
q = 4, r = 6, and
(g) 5(2p + q)
p

21. Evaluate the following given p = 2
q = 4, r = 6, and
(h) 2p (2p + 7)
3