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Expressions

Tidy up algebra: collect like terms, expand brackets and factorise. Simplifying first makes every equation easier to solve.

  • Collect like terms
  • Expand single brackets
  • Factorise simple expressions

Tidying algebra

Simplifying rewrites an expression in its neatest form without changing its value. It's the algebraic equivalent of tidying your desk before starting work — everything afterwards gets easier.

Like terms

Like terms have exactly the same variable parts. 3x and 5x are like terms; 3x and 3x² are not (different powers); 2ab and 3ba are (multiplication commutes).

Maths
3x + 5x = 8x                  like terms combine
4a + 2b − a = 3a + 2b          a-terms combine; b stays
2x + 3x² → cannot combine      different powers
Fruit salad algebra

Think of x as apples and y as bananas: 3 apples + 2 apples = 5 apples, but 3 apples + 2 bananas can't combine. Silly, but it never fails.

Expanding brackets

Multiply everything inside the bracket by what's outside:

Maths
3(x + 4) = 3x + 12
−2(5 − y) = −10 + 2y
x(x + 3) = x² + 3x
Signs

A minus outside the bracket flips every sign inside: −(a − b) = −a + b. This is where most errors happen — expand slowly and check each sign.

Factorising

Factorising is expanding in reverse: pull out the common factor.

Maths
6x + 9 = 3(2x + 3)        3 is the highest common factor
4a² − 8a = 4a(a − 2)      take out 4a

To check, expand your answer — you should get back where you started.

Worked example

Simplify 3(x + 2) + 2x.

Expand first, then collect like terms:

Maths
3(x + 2) + 2x = 3x + 6 + 2x = 5x + 6

Practice

Simplify: 7p − 2p + 4.
Combine the p-terms.

5p + 4.

Expand: 5(2x − 3).
Multiply both terms by 5.

10x − 15.

Factorise: 8y + 12.
What divides both 8 and 12?

4(2y + 3).

Simplify: 2(a − 3) − (a + 5).
Watch the minus before the second bracket.

2a − 6 − a − 5 = a − 11.

Quick check

Expressions — quick check

Simplify 6m + 2 − 4m.

6m − 4m = 2m; the constant 2 stays: 2m + 2.

Expand −4(x − 5).

−4 × x = −4x; −4 × −5 = +20.

Factorise 9x − 6.

The highest common factor is 3: 3(3x − 2). Expand to check.
Key takeaways
  • Combine like terms — identical variable parts only.
  • Expand brackets by multiplying through; watch the signs.
  • Factorising pulls out the common factor — expanding reverses it.
  • Simplify before solving: tidy expressions make equations easier.
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