Year 10 - Maths
Factorising a quadratic expression
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 factorise quadratics of the form x^2 + bx + c.
Key Notes
- The distributive law can be used to find the two factors of a quadratic expression with three non-zero terms.
- An area model can be used to explore the underlying structure.
- You can check your factors by finding the product and checking it against the quadratic.
Vocabulary To Learn
- Factorise: To express a term as the product of its factors.
- Quadratic: A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2
Common Mistakes To Avoid
- Pupils often get signs the incorrect way round in the binomials. E.g. (x+2)(x-4) instead of (x-2)(x+4)
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The distributive law can be used to find the two factors of a quadratic expression with three non-zero terms. An area model can be used to explore the underlying structure.
2. Use this key word in a maths sentence and explain it clearly. 'Factorise'
To express a term as the product of its factors. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils often get signs the incorrect way round in the binomials. E.g. (x+2)(x-4) instead of (x-2)(x+4). Correction: Encourage pupils to always expand their binomials to check they are correct. Using representations such as an area model should reduce the likelihood of this as pupils focus on the structure and reason behind their choices.
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 factorising 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 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
Browse all guides in the Year 10 Maths guide library.