PROBLEM SOLVING

Collecting Like Terms

Learn the reliable method for collecting like terms, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Like terms have the same variable part and can be combined.

Picture itFollow what happens to the unknown
2 · THE METHOD

Follow these steps

  1. Group terms with the same variable and exponent.
  2. Add or subtract their coefficients.
  3. Keep unlike terms separate and simplify constants independently.
3 · WORKED EXAMPLES

See the method in action

Example 1

A triangle has sides 4x+3, 5x−1 and 6x+2. Which expression gives its perimeter?

  1. Add coefficients: 4+5+6=15.
  2. Add constants: 3−1+2=4.
Answer: 15x + 4
Example 2

7 packs each contain x red and 6 blue counters. Which expression gives the total counters?

  1. Each pack has x+6.
  2. Multiplying both terms by 7 gives 7x+42.
Answer: 7x + 42
4 · ELEVENSPRINT TIP

A useful shortcut

Keep unlike terms separate and simplify constants independently.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.