Form 1 Unit 8:Lesson 4- Multiplication and Division of Algebraic Expressions
Objective
At the end of the lesson, the students should be able to simplify algebraic expressions involving multiplication and division.
In performing multiplication and division of algebraic expressions it is important to first multiply the number, then the letters. When you have like terms in the expression, you simplify them.
Multiplication and Division of Algebraic Expressions by a Number (constant).
In multiplication or division of algebraic expressions 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.
In algebraic expression, division can be expressed as
Therefore when dividing algebraic expressions, it is written in the form 
even when it is given as
or a ÷ b.
This is done to make calculation easier.
Example 1
Simplify the following:
a) 2x ÷ 2 b) 4m ÷ 3 c) (3x+5) ÷ 5
Solution
Multiplication and Division of Algebraic Expressions by a Number and a Letter
It is important to first group the numbers with the same letter together and apply the basic operating rules of indices. After multiplication, the letters are written in alphabetical order.
To simplify with exponents, it is often simpler to work directly from the definition and meaning of exponents. For instance:
Simplify x6 × x5
Just thought about what exponents mean. The ” x6 ”
means “six copies of x multiplied together”, and the ” x5 ” means “five copies of x multiplied together”. So if I multiply those two expressions together, I will get eleven copies of x multiplied together. That is:
x6 × x5 = (x6)(x5)
= (xxxxxx)(xxxxx) (6 times, and then 5 times)
= xxxxxxxxxxx (11 times)
= x11
Thus: x6 × x5 =x(6+5)= x11
Simplify 
Example 1
Simplify the following:
- a) 2a2 x 5a3 b) y x 4y x 3y c) 3c2×3c3
Solution 1
a) 2a2×5a3 Multiply the same variable using powers.
= (2×5)a(2+3) The indices are added together
=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 Deal with the bracket first.
Example 2
a) 2x ×3y × 5z b) –3x × 2y
Solution
a) 2x ×3y × 5z
2x × 3y × 5z multiply the numbers, and rewrite the letters
= (2×3× 5)xyz
= 30xyz.
b) –3x × 2y
–3x × 2y multiple the number and multiple the letters
= (–3×2)x × y
= –6xy
Therefore –3x × 2y=–6xy
Example 3
Simplify the following:
a) 2y x 6e x 3zy b) 3xy2 × 4x3y4
Solution
a) 2y x 6e x 3zy
= (2×6×3)y × y × e × z always arrange letters in alphabetical order
= 36ey2z
b) 3xy2 × 4x3y4
=3×4x×x3×y2×y4
=(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 number of times the variable appears.
Example 1
Simplify the following:
Solution
Don’t forget that the “7” and the “3” are just numbers. Since 3 doesn’t go evenly into 7, we can’t cancel the numbers. The 7/3 stays as it is. For the variables, we have three extra copies of x on top, so the answer is: 
Numbers cancel out numbers and like variables also cancel out. For the above example, s2 cancels out s2 out of s3 leaving one “s”.
Like terms can be cancelled out, one of x the will be cancelled from the x2 leaving only one x. The answer therefore becomes