This document discusses algebraic expressions and how to work with them. It covers writing expressions from word problems, identifying unknowns, determining the number of terms, simplifying by collecting like terms, and evaluating expressions by substituting values. Examples are provided for each concept to demonstrate the process. Key steps include identifying like terms, combining them, and substituting values for variables into expressions to calculate numerical results.

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