 # 4.02 Multiplying and dividing algebraic terms

Lesson

## Multiplication and division of algebraic terms

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\times x=x^2.

• When dividing, cancel any common factors. For example, x\div x=1.

3. 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.

### Examples

#### Example 1

Simplify the expression 7\times u\times v\times 9.

Worked Solution
Create a strategy

Multiply the coefficients and combine the pronumerals into one term.

Apply the idea

#### Example 2

Simplify the expression \dfrac{15yw}{5y}.

Worked Solution
Create a strategy

Cancel out any common factors in the numerator and denominator.

Apply the idea

The coefficients 15 and 5 have a highest common factor of 5. The variable y is also a common factor for both the numerator and denominator.

Idea 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\times x=x^2.

• When dividing, cancel any common factors. For example, x\div x=1.

3. 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.

### Outcomes

#### MA4-9NA

operates with positive-integer and zero indices of numerical bases