Year 10 - Maths
Checking and securing understanding of factorising
Algebraic manipulation
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In algebraic manipulation, pupils use apply knowledge of the distributive law to find the product of two binomaials in order to factorise quadratics.
Lesson Summary
You will learn to use the distributive law to factorise expressions where there is a common factor.
Key Notes
- An expression can be described as being factorised.
- An expression is fully factorised if the highest common factor has been taken out.
- The distributive law can help us factorise an expression.
Vocabulary To Learn
- Factor: A factor is a term which exactly divides another term.
- Factorise: To factorise is to express a term as the product of its factors.
Common Mistakes To Avoid
- Leaving answers which are not fully factorised when they are required to.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
An expression can be described as being factorised. An expression is fully factorised if the highest common factor has been taken out.
2. Use this key word in a maths sentence and explain it clearly. 'Factor'
A factor is a term which exactly divides another term. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Leaving answers which are not fully factorised when they are required to. Correction: There should be a focus on reading questions to decipher what they are being asked to do. When they have to fully factorise they need the highest common factor of all the terms. LC3 focuses on situations where they are not going to fully factorise.
More Lessons In This Unit
- Advanced problem solving with algebraic manipulation Study Guide
- Checking and securing understanding of changing the subject Study Guide
- Checking and securing understanding of expanding a single bracket Study Guide
- Checking and securing understanding of forming linear equations Study Guide
- Checking and securing understanding of simplifying Study Guide
- Checking and securing understanding of solving and interpreting linear equations Study Guide
- Checking and securing understanding of substitution Study Guide
- Checking and securing understanding of the product of two binomials Study Guide
- Factorising a quadratic expression Study Guide
- Factorising quadratics of the form ax^2 + bx + c Study Guide
- Factorising using the difference of two squares Study Guide
- Further algebraic terminology Study Guide
- Problem solving with algebraic manipulation Study Guide
- Solving complex quadratic equations by completing the square Study Guide
- Solving quadratic equations by completing the square Study Guide
- Solving quadratic equations by factorising Study Guide
- Solving quadratic equations by factorising where rearrangement is required Study Guide
- Solving quadratic equations by using the formula Study Guide
- The product of three binomials Study Guide
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