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6. Algebra
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iGCSE (2021 Edition)

6.07 Multiplying and dividing terms

Lesson
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Lesson

We multiply and divide algebraic terms using this process:

  1. Split each term into its coefficient and its pronumerals.
  2. Find the product or quotient of the coefficient of the terms.
    • When multiplying, combine like factors into a power. For example, $$x×x=x2.
    • When dividing, cancel any common factors. For example, $$x÷​x=1.
  4. Combine the coefficient and pronumerals into one term.

Unlike adding and subtracting, when we multiply or divide algebraic terms, we can collect them into one term.

Worked Examples

Example 1

Simplify $$6x×9y.

Think: Here we have a product of algebraic terms, so we can follow the process above to simplify this.

Do: $$6x has a coefficient of $$6 and a pronumeral $$x. $$9y has a coefficient $$9 and a pronumeral $$y.

We first want to evaluate the product of the coefficients. Here we have $$6×9=54.

Next we look at the pronumerals in each term. $$6x has $$x but not $$y and $$9y has $$y but not $$x. So we cannot simplify the pronumerals any further.

This leaves us with the factors $$54, $$x, and $$y. We can simplify this without writing the multiplication signs to get $$54xy.

Example 2

Simplify $$6xz÷​(9yz).

Think: Here we have a quotient of algebraic terms, so we can follow the same process as above except that we divide instead of multiplying.

We can also write this division as the fraction $$6xz9yz​ which will make the simplification easier.

Do: $$6xz has a coefficient of $$6 and the pronumerals $$x and $$z. $$9yx has a coefficient $$9 and the pronumerals $$y and $$z.

We first want to simplify the quotient of the coefficients. Here we have $$69​=23​.

Next we simplify the pronumerals. If we take just the pronumeral part of the fraction above we get $$xzyz​. $$z is common to both the numerator and the denominator so we can cancel out $$z, but we can't cancel out $$x or $$y.

This leaves us with the factors $$23​ and $$xy​. We can simplify this into the fraction $$2x3y​.

Summary

We multiply and divide algebraic terms using this process:

  1. Split each term into its coefficient and its pronumerals.
  2. Find the product or quotient of the coefficient of the terms.
    • When multiplying, combine like factors into a power. For example, $$x×x=x2.
    • When dividing, cancel any common factors. For example, $$x÷​x=1.
  4. Combine the coefficient and pronumerals into one term.

Unlike adding and subtracting, when we multiply or divide algebraic terms, we can collect them into one term.

Practice questions

Question 1

Simplify the expression $$9×m×n×8.

Question 2

Simplify the expression $$6u2×7v8.

Question 3

Simplify the expression $$63pq9p​.

 

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