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Factorising | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Basic Factorising

What is factorisation?

  • A factorised expression is one that is written as the product (multiplication) of two or more terms (factors). For example:
    • 3(x + 2) is factorised as it is 3 x (x + 2).
    • 3x + 6 is not factorised because it is a single term.
    • 3xy is factorised as 3 x x x y.
    • 12 can also be factorised as 12 = 2 x 2 x 3.
  • In algebra, factorisation is the opposite of expanding brackets; it involves putting an expression into brackets.

How do I factorise two terms?

To factorise an expression like 12x2 - 18x, we follow these steps:

  • Identify the highest common factor of the coefficients and the variables separately. 
  • For 12 and 18, the HCF is 6. 
  • For xand x, it is x.
  • Multiply these common factors to get 6x.
  • Rewrite each term as the common factor multiplied by something else: 6x x 2x and 6x x 3.
  • Take out the common factor (6x) by writing it outside the brackets and put the remaining terms inside. 
  • The answer is 6x(2x - 3).
  • Check this expands to give 12x+ 18x

Factorising by Grouping

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How to Factorise Expressions with Common Brackets 

  • When you are asked to factorise expressions like 3x(t - 4) + 2(t - 4), you may notice that both terms share a common bracket, (t - 4). 
  • This common bracket can be "taken out" as a common factor, resulting in (t - 4)(3x + 2). 
  • This process is similar to factorising expressions like 3xy + 2y, where you factor out the common factor y to get y(3x + 2). 
  • Here, y represents (t - 4).
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How do I factorise by grouping?

  • When factorising by grouping, you may need to create a common bracket.
    • For instance, consider the expression: xy + px + qy + pq.
    • Group the first pair of terms, xy and px, and factorise to get x(y + p).
    • Next, group the second pair of terms, qy and pq, and factorise to obtain q(y + p).
    • Now, factorise x(y + p) and q(y + p) together to get (y + p)(x + q).
  • This method is known as factorizing by grouping.
  • The groupings don't always consist of the first and second pairs of terms but rather any two terms that share common factors.

Question for Factorising
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Factorize the expression 4x + 8.
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FAQs on Factorising - Mathematics for GCSE/IGCSE - Year 11

1. What is the purpose of factorising in mathematics?
Ans. Factorising is a technique used in mathematics to simplify expressions by breaking them down into smaller factors. This can help in solving equations, finding common factors, and simplifying complex expressions.
2. How do you factorise by grouping in algebra?
Ans. To factorise by grouping, you first group the terms in pairs and then factor out the common factor from each pair. Finally, factor out the common factor that remains after grouping to simplify the expression.
3. Can factorising help in solving quadratic equations?
Ans. Yes, factorising can be very helpful in solving quadratic equations. By factoring the quadratic expression into two binomials, you can easily find the roots of the equation and solve for the unknown variable.
4. What are some common techniques used for factorising in Year 11 mathematics?
Ans. Some common techniques for factorising in Year 11 mathematics include factorising by grouping, difference of squares, perfect square trinomials, and trial and error method.
5. Why is it important to understand factorising in Year 11 mathematics?
Ans. Understanding factorising is important as it forms the basis for solving various types of equations and simplifying algebraic expressions. It is a fundamental skill that is used in higher-level mathematics courses and real-life applications.
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