Algebraic Manipulation

Ages 16–18

Difficulty adapts to you

Algebraic Manipulation

An expression is a calculation without an equals sign. Collect like terms, expand brackets using multiplication, and factorise by reversing expansion. When rearranging a formula, perform the same legal operation on both sides.

Your goals

✓You can simplify, expand, factorise, and rearrange expressions while preserving equality.
✓You can use Algebraic Manipulation, model correctly.
✓You can use the definitions, units, assumptions, and examples to check your answer.

Words to know

Algebraic Manipulation:: Simplify, expand, factorise, and rearrange expressions while preserving equality.
model:: A rule or representation used to describe a situation and make a prediction.

Examples

13x + 5x − 2 = 8x − 2.
2(x + 3)(x + 2) = x² + 5x + 6.
3From v = u + at, subtract u and divide by a to make t the subject.

Check these

• Do not skip the meaning of a term or give a result without explaining what it means.
• Keep every number, symbol, label, and unit in its correct place.
• Show enough working to check how you reached your answer.

Helpful habits

• Read the whole question before choosing what to do.
• Show one clear step at a time and check each step.
• If you are stuck, draw a model, try smaller numbers, or revisit the example.

Now try your own

Create your own algebraic manipulation example, solve it, and explain how you checked it.

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Helpful Hints

“Try drawing a picture to help you see the answer.”