Form 2 Unit 2 Lesson 4 – Multiplication and Division of Algebraic Expression

Objective

At the end of the lesson, the students should be able to:
Simplify algebraic expressions involving multiplication and division.
In multiplying and dividing algebraic expressions, it is important to first multiply the numbers, then the letters.

Multiplication and division of algebraic expressions by a number (constant).
When multiplying or dividing algebraic expression by a number, you don’t have to worry about whether the variables are the same or not, all you have to do is multiply or divide every expression.

Example 1
Simplify
a) 2 × t                 b) m × 2                c) 2t × 5

Solution
a) 2 × t = 2t           b) m × 2 = 2m     c) 2t × 5 = 10t
The convention is to write the number first then the letters.

Example 2
Simplify the following;
a) 2x÷2                  b) 4m÷3                         c) (3x+5)÷5

Solution
a) 2x÷2 `                b) 4m ÷3                       c)(3x+5)÷5
= ^2x/₂                        =⁴/₃m                           =³/₅ x + ⁵/₅
=x                                                                       =³/₅x + 1

Multiplication and division of algebraic expressions by a number and a letter
It is important to first group the number and the same letter together and apply the basic operating rules of indices. After multiplication, the letters are written in alphabetical order

Example 1
Simplify the following:
a) 2a² x 5a³                             b) y x 4y x 3y                 c) 3c² × 3c³               d) (8d³ × 2d⁵)÷4d²               e) 2y x 6e x 3zy

Solution
a) 2a²×5a³
= (2×5)a⁽²⁺³⁾          (multiply the same variables, add the powers)
=10a⁵     
b) y x 4y x 3y
= (1×4×3)y ^(1+1+1)
=12Y³
Note that, y is the same as 1y.
c) 3c² × 3c³
=3 × 3c ⁽²⁺³⁾
=9c⁵

d) (8d³ × 2d⁵) ÷ 4d²
= (8 × 2d ⁽³⁺⁵⁾) ÷4d²              (Deal with the bracket first)
= 16d⁸ ÷ 4d²
=   ¹⁶/₄ d^8–2
   = 4d⁶

e) 2y x 6e x 3zy
= (2×6×3⁾ y×y×e×z       
     (Always arrange letters in alphabetical order)
= 36ey²z

Example 2
Simplify the following:
a) -3x×2y           b) 3xy²×4x ³y⁴

Solution 2
-3x × 2y
(Multiply the numbers then multiply the letters)
= (-3×2) x ×y
= -6xy
Therefore -3x × 2y = -6xy
b) 3xy² × 4x³y⁴
= (3×4) x⁽¹⁺³⁾ y⁽²⁺⁴⁾                           remember x=x¹
=12x⁴y⁶
Therefore 3xy² × 4x³y⁴ = 12x⁴y⁶
When you have the same variable appearing more than once, you raise the variable to the power of the number of times the variable appears.