Year 10 - Maths
Factorising using the difference of two squares
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 including using the difference of two squares.
Key Notes
- When the coefficient of the x term is zero, you may still be able to factorise.
- There is a structure to the quadratic expressions that can be factorised if there is no x term.
- The same area model can be used to explore this structure.
Vocabulary To Learn
- Factorise: To factorise is 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
- Absolute value: The absolute value of a number is its distance from zero.
Common Mistakes To Avoid
- Once shown the difference of two squares, pupils may think that squaring each term in a binomial is the correct way to expand binomials such as (x+3)^2
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When the coefficient of the x term is zero, you may still be able to factorise. There is a structure to the quadratic expressions that can be factorised if there is no x term.
2. Use this key word in a maths sentence and explain it clearly. 'Factorise'
To factorise is 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: Once shown the difference of two squares, pupils may think that squaring each term in a binomial is the correct way to expand binomials such as (x+3)^2. Correction: Spend time investigating where the difference of two squares occurs, use representations such as algebra tiles and area models.
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 a quadratic expression Study Guide
- Factorising quadratics of the form ax^2 + bx + c 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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