Factorising Out Terms (Edexcel IGCSE Maths)

Basic Factorising

Spec point — 2.2D

What is factorisation?

• A factorised expression is one written as the product (multiplication) of two, or more, terms (factors)

  • 3(x + 2) is factorised

    • It is 3 × (x + 2)

  • 3x + 6* * is not factorised

  • 3*xy * is factorised

    • It is 3 × x × y

  • Numbers can also be factorised

    • 12 = 2 x 2 x 3

• In algebra, factorisation is the reverse of expanding brackets

  • It's putting it into brackets, rather than removing brackets

How do I factorise two terms?

• To factorise 12x² + 18*x *

  • Find the highest common factor of the number parts

    • 6

  • Find the highest common factor of the algebra parts

    • x

  • Multiply both to get the overall highest common factor

    • 6x

  • 12x² + 18x * is the same as 6x * × 2x + 6x × 3

    • Using the highest common factor

  • Take out the highest common factor

    • Write it outside a set of brackets
    • Put the remaining terms, 2*x * + 3, inside the brackets

  • This gives the answer

    • 6x (2x + 3)

• To factorise an expression containing multiple variables, e.g. 2a³b - 4a²b²

  • Use the same approach as above

  • Find the highest common factor of the number parts

    • 2

  • Find the highest common factor of the algebra parts

    • a and b appear in both terms
    • The highest common factor of a³ and a² is a²
    • The highest common factor of b and b² is b
    • a²b

  • Multiply both to get the overall highest common factor

    • 2a²b

  • 2a³b - 4a²b²* * is the same as 2a²b × a - 2a²b × 2b

    • Using the highest common factor

  • Take out the highest common factor

    • Write it outside a set of brackets
    • Put the remaining terms, a - 2b, inside the brackets

  • This gives the answer

    • 2a²b (a - 2b)

Exam Hint In the exam, check that your factorisation is correct by expanding the brackets.

Factorise means factorise fully.

x (6*x + 10) is not fully factorised but 2x (3x *+ 5) is.

Worked Example (a) Factorise 5x + 15 Answer:

Find the highest common factor of 5 and 15

5

There is no x in the second term, so no highest common factor in x is needed Think of each term as 5 × something

5 × x + 5 × 3

*Take out the 5 and put **x *+ 3 in brackets

Final answer: 5(x + 3)

(b) Factorise fully 30x² - 24x

Answer:

Find the highest common factor of 30 and 24

6

*Find the highest common factor of x² and *x

x

Find the overall highest common factor by multiplying these together

*6x

Think of each term as 6x × something

6x × 5x - 6x × 4

Take out the 6x and put 5x - 4 in brackets

Final answer: 6x (5x - 4)

(c) Factorise fully 5x⁴y + 25x³y³

Answer:

Find the highest common factor of 5 and 25

5

*Find the highest common factor of x⁴ and *x³

x³*

*Find the highest common factor of y and *y³

y

Find the overall highest common factor by multiplying these together

*5x³y

Think of each term as 5**x³*y *× something

5x ³y × x + 5x ³y × 5y²

Take out the 5**x³y* and put x + 5**y*² in brackets

Final answer: 5x ³y (x + 5y²)