Simplifying expressions | Year 10

01 / LEARN

The idea, step by step

Which terms can be combined?

A term includes its sign, numerical coefficient and variable part. Terms are like terms only when their variables and powers match. For example, $4 x$ and $- 7 x$ can be combined, but $4 x$ and $4 x^{2}$ cannot. Keep unlike terms as separate parts of the answer.

Simplifying in a reliable order

Expand brackets if needed, then group like terms and add their coefficients. A minus sign before a bracket changes every sign inside it. Multiplication uses exponent laws, whereas addition combines coefficients: $3 x + 2 x = 5 x$ , but $3 x \times 2 x = 6 x^{2}$ . Check an answer by substituting a simple value into both forms.

A common trap

$3 x + 4 x^{2} = 7 x^{3}$ .

Instead: These are unlike terms. Addition does not add exponents, so the expression stays $4 x^{2} + 3 x$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Collect coefficients

$7 a - 3 b - 2 a + 5 b$

Group the $a$ terms: $7 a - 2 a = 5 a$ .
Group the $b$ terms: $- 3 b + 5 b = 2 b$ .

5 a + 2 b

Example 2

Keep powers distinct

Simplify $4 x^{2} - 3 x + 6 - 2 x^{2} + 5 x - 9$ .

Combine the square terms: $4 x^{2} - 2 x^{2} = 2 x^{2}$ .
Combine the linear terms: $- 3 x + 5 x = 2 x$ .
Combine constants: $6 - 9 = - 3$ .

2 x^{2} + 2 x - 3

Check your understanding

Simplify $6 p - 2 q - 9 p + 5 q$ .

Show answer

$- 3 p + 3 q$

The coefficients of $p$ add to $- 3$ and those of $q$ add to $3$ .

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Simplify $9 x - 4 x + 2 x$ .
2 marks
Simplify $5 a + 3 b - 2 a + 4 b$ .
2 marks
Simplify $8 m^{2} - 3 m + 2 m^{2} + 7 m$ .
2 marks
Simplify $4 p - (3 p - 5)$ .
2 marks
A rectangle has adjacent sides $3 x + 2$ cm and $x + 5$ cm. Write its perimeter in simplified form.
3 marks
Rina says $2 x + 5 y = 7 x y$ . Explain the error and test the claim using $x = 2, y = 1$ .
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Simplify $9 x - 4 x + 2 x$ .
2 marks
Add coefficients: $9 - 4 + 2 = 7$ .
$7 x$
Simplify $5 a + 3 b - 2 a + 4 b$ .
2 marks
Collect $5 a - 2 a$ and $3 b + 4 b$ .
$3 a + 7 b$
Simplify $8 m^{2} - 3 m + 2 m^{2} + 7 m$ .
2 marks
Collect equal powers separately.
$10 m^{2} + 4 m$
Simplify $4 p - (3 p - 5)$ .
2 marks
The subtraction gives $4 p - 3 p + 5$ .
$p + 5$
A rectangle has adjacent sides $3 x + 2$ cm and $x + 5$ cm. Write its perimeter in simplified form.
3 marks
$P = 2 (3 x + 2) + 2 (x + 5)$ .
Expand and collect: $6 x + 4 + 2 x + 10 = 8 x + 14$ .
$8 x + 14$ cm
Rina says $2 x + 5 y = 7 x y$ . Explain the error and test the claim using $x = 2, y = 1$ .
3 marks
The variable parts $x$ and $y$ differ.
Substitution gives $2 (2) + 5 (1) = 9$ , while $7 (2) (1) = 14$ .
Unlike terms cannot be combined. The original equals $9$ ; $7 x y$ equals $14$ .

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Curriculum reference & lesson scope

Australian Curriculum v9 and South Australian Mathematics Curriculum

Year 10 algebra, including the approved fuller school-course treatment of rational expressions and formula restrictions; quadratic methods are in their own chapter.

Official curriculum source ↗

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