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Year 10 Interactive Maths - Second Edition


Expressions

To solve a problem we need to find the value of an unknown quantity or quantities.  The unknown quantity or quantities are represented by letters that are known as pronumerals.

An expression is a combination of mathematical terms using operations such as addition, subtraction, multiplication, division, brackets, powers or roots.  

For example, 2x + 3y is an expression involving addition where 2x and 3y are called the terms of the expression.  Terms often include pronumerals but may also be a number called a constant term.

Terms with the same pronumeral or pronumerals are called like terms.

Examples of algebraic expressions consisting of like terms.

Terms that do not have the same pronumerals are called unlike terms.

Examples of algebraic expressions consisting of unlike terms.


Addition and Subtraction

Only like terms can be added (or subtracted) to simplify an expression involving addition (or subtraction).

Example 1

Simplify six different algebraic expressions.

Solution:

Collect like terms to simplify the algebraic expression in example 1a.

Collect like terms to simplify the algebraic expression in example 1b.

Collect like terms to simplify the algebraic expression in example 1c.

Collect like terms to simplify the algebraic expression in example 1d.

Collect like terms to simplify the algebraic expression in example 1e.

Collect like terms to simplify the algebraic expression in example 1f.


Key Terms

pronumerals, expression, terms, constant term, like terms, unlike terms


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