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Sec 1 Algebraic Expressions | Terms, Like Terms, Substitution and Simplification

Secondary 1 Algebraic Expressions turns arithmetic patterns into a general mathematical language. Instead of working with one particular number, algebra lets students describe relationships that work for many possible values. The challenge is learning to read the structure of an expression rather than treating letters as mysterious objects.

Students searching for Sec 1 algebra, algebraic expressions, like terms, coefficients, substitution or simplifying expressions often memorise rules such as “collect like terms”. The stronger method is to identify what each term represents, which terms are alike, and which operations connect them.

This page is the canonical Algebraic Expressions owner under the Secondary Mathematics Topic Library. It grows directly from Primary 6 Algebra and leads into Linear Equations.

Quick answer: the vocabulary

  • Variable: a letter representing a number.
  • Constant: a fixed number.
  • Term: a part separated by + or −.
  • Coefficient: the numerical factor multiplying a variable.
  • Like terms: terms with the same variable part.
  • Expression: a mathematical phrase without an equals sign.

Read expressions as grouped quantities

In 3x + 5, the expression has two terms: 3x and 5.

3x means 3 × x. The number 3 is the coefficient of x.

The +5 is a constant term.

Like terms

4x + 7x = 11x because both terms count the same kind of quantity x.

4x + 7y cannot be combined because x and y may represent different quantities.

Similarly, 3x and 3x² are not like terms because x and x² are different variable parts.

Worked example 1: simplify

Simplify: 5a + 3a − 4.

5a + 3a = 8a, so the simplified expression is 8a − 4.

Worked example 2: multiple variables

Simplify: 4x + 2y − x + 5y.

x terms: 4x − x = 3x.
y terms: 2y + 5y = 7y.

Answer: 3x + 7y.

Substitution

Substitution means replacing a variable with a known value.

Expression: 2x + 5, where x = −3.

2(−3) + 5 = −6 + 5 = −1.

The brackets around −3 protect the sign.

Multiplication notation

  • 3 × x is written 3x
  • a × b is written ab
  • 2 × x × y is written 2xy
  • x × x is written x²

But x + x = 2x, while x × x = x². Addition and multiplication create different structures.

Removing brackets

At an introductory level, if a number multiplies a bracket, it multiplies every term inside.

Example: 3(x + 4) = 3x + 12.

This is the distributive law. It prepares students for expansion in later Secondary Mathematics.

Negative signs before brackets

A negative sign in front of a bracket changes the sign of every term when the bracket is removed.

−(x + 3) = −x − 3.

This is a common source of error because students change only the first term.

Worked example 3: expand and simplify

Simplify: 2(x + 3) + 4x.

Expand: 2x + 6 + 4x.

Collect like terms: 6x + 6.

Expression versus equation

3x + 7 is an expression. 3x + 7 = 19 is an equation.

Expressions are simplified or evaluated. Equations are solved for values that make the equality true.

Translating words into algebra

five more than x

Expression: x + 5

three times y

Expression: 3y

seven less than twice n

Expression: 2n − 7

the total cost of x items at $4 each

Expression: 4x

the perimeter of a rectangle with length x and width 3

Expression: 2x + 6

Order matters in subtraction

“5 less than x” means x − 5, not 5 − x.

“x is 5 less than y” means x = y − 5.

Language direction must be understood, not translated word by word.

Common expression errors

  • adds coefficients of unlike terms
  • turns x + x into x²
  • forgets brackets around negative substitution
  • distributes multiplication to only one term
  • changes only one sign after a negative bracket
  • confuses expression with equation
  • reverses subtraction language

The expression check

  1. Identify the terms.
  2. Mark like terms.
  3. Expand brackets if needed.
  4. Collect like terms.
  5. Check signs.
  6. If substituting, use brackets for negative values.
  7. Estimate whether the result is sensible.

Transfer into equations

Expressions describe relationships. Equations state that two expressions are equal. Once students can simplify expressions reliably, solving equations becomes much easier because both sides can be reduced before inverse operations are applied.

Practice

Practice 1

Question: 3x + 5x

Answer: 8x

Practice 2

Question: 6a + 2b − 4a + b

Answer: 2a + 3b

Practice 3

Question: If x=4, find 3x−2

Answer: 10

Practice 4

Question: 2(y+5)

Answer: 2y+10

Practice 5

Question: −(m−7)

Answer: −m+7

Practice 6

Question: 4x + 3 = 19

Answer: This is an equation, not just an expression.

Frequently asked questions

What are like terms?

Terms with the same variable part, such as 3x and −5x.

Can x and x² be combined?

No. They are unlike terms.

Why does 3(x+2) become 3x+6?

Because multiplication distributes across every term inside the bracket.

Why are negative substitutions written in brackets?

To show that the sign belongs to the value and prevent operation errors.

Where does this sit in Atlas?

This is the canonical Sec 1 Algebraic Expressions owner under Secondary Mathematics Topic Library.

The final Expressions rule

Read algebra as structure. Identify terms, respect signs, combine only like quantities and use substitution as a meaning check. Expressions are the grammar of the algebra students will use throughout Secondary Mathematics.

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