Split each term into its coefficient and its pronumerals.
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.
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.

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

\displaystyle 7\times u\times v\times 9	\displaystyle =	\displaystyle 7\times9\times u\times v	Rearrange the terms
	\displaystyle =	\displaystyle 63uv	Evaluate the multiplication

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.

\displaystyle \dfrac{15yw}{5y}	\displaystyle =	\displaystyle \dfrac{15yw \div 5}{5y \div 5}	Divide the numerator and denominator by 5
	\displaystyle =	\displaystyle \dfrac{3yw}{y}	Evaluate
	\displaystyle =	\displaystyle 3w	Cancel out y

Idea summary

We multiply and divide algebraic terms using this process:

Split each term into its coefficient and its pronumerals.
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.
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.

8.06 Multiplying and dividing algebraic terms

Ideas