Topics
8 Patterns and algebra
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AustraliaNSW
Stage 4

8.07 Simplifying algebraic expressions

Lesson
Worksheet
Practice
Lesson

Simplify algebraic expressions

We simplify algebraic expressions following the same order of operations as for numeric expressions. That is,

  1. Simplify any expression in brackets first.

  2. Simplify any powers.

  3. Simplify any multiplication or division from left to right.

  4. Simplify any addition or subtraction from left to right.

Examples

Example 1

Simplify the expression 4s+9\times 5s.

Worked Solution
Create a strategy

Use the order of operations.

Apply the idea
\displaystyle 4s+9\times 5s\displaystyle =\displaystyle 4s+45sEvaluate the multiplication
\displaystyle =\displaystyle 49sEvaluate the addition

Example 2

Simplify the expression 12s-8s\div 4.

Worked Solution
Create a strategy

Use the order of operations.

Apply the idea
\displaystyle 12s-8s\div 4\displaystyle =\displaystyle 12s-2sDivide -8s by 4
\displaystyle =\displaystyle 10sEvaluate the subtraction
Idea summary

We simplify algebraic expressions following the same order of operations as for numeric expressions:

  1. Simplify any expression in brackets first.

  2. Simplify any powers.

  3. Simplify any multiplication or division from left to right.

  4. Simplify any addition or subtraction from left to right.

Outcomes

MA4-8NA

generalises number properties to operate with algebraic expressions

MA4-9NA

operates with positive-integer and zero indices of numerical bases

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