Introduction to Factorising Brackets

Hello, everyone! Today, we are going to learn about factorising brackets. This is an important skill in maths that helps us simplify expressions and solve equations more easily.

What Does Factorising Mean?

Factorising means breaking down an expression into simpler parts, called factors. When we factorise, we look for numbers or letters that can be multiplied together to give us the original expression.

Why Do We Use Brackets?

Brackets are used in maths to show that certain operations should be done first. When we factorise, we often put factors in brackets to show how they combine to make the original expression.

Key Rules for Factorising Brackets

  1. Look for Common Factors: Always check if there is a number or letter that is common in each term of the expression. For example, in the expression 2x + 4
    , both terms share a common factor of 2.
  2. Divide by the Common Factor: Once you find the common factor, divide each term by it. For 2x + 4
    , we divide both terms by 2.
  3. Write in Brackets: After dividing, write the common factor outside the brackets and the remaining terms inside. So, 2x + 4
    becomes 2(x + 2)
    .

Example of Factorising Brackets

Let’s look at an example:

Example 1: Factorise 6y + 9

.

  1. Find the Common Factor: The common factor is 3.
  2. Divide: 6y ÷ 3 = 2y
    and 9 ÷ 3 = 3
    .
  3. Write in Brackets: The factorised form is 3(2y + 3)
    .

Tips for Factorising

  • Always start by looking for the highest common factor.
  • If there are letters involved, check if they share a common variable.
  • Practice makes perfect! The more you factorise, the better you will get.

Practice Questions

Easy Level Questions

  1. Factorise 4x + 8
    .
  2. Factorise 3a + 6
    .
  3. Factorise 5b + 10
    .
  4. Factorise 2m + 4
    .
  5. Factorise 7x + 14
    .
  6. Factorise 9y + 12
    .
  7. Factorise 10a + 15
    .
  8. Factorise 6x + 3
    .
  9. Factorise 8p + 16
    .
  10. Factorise 4z + 20
    .

Medium Level Questions

  1. Factorise 12x + 18
    .
  2. Factorise 15b + 10b
    .
  3. Factorise 14a + 21
    .
  4. Factorise 8m + 4n
    .
  5. Factorise 9x + 27
    .
  6. Factorise 6y + 15y
    .
  7. Factorise 10p + 25
    .
  8. Factorise 5a + 20b
    .
  9. Factorise 4x + 16y
    .
  10. Factorise 20k + 15
    .

Hard Level Questions

  1. Factorise 4x^2 + 8x
    .
  2. Factorise 6a^2 + 12a
    .
  3. Factorise 10x^2 + 15x
    .
  4. Factorise 9y^2 + 27y
    .
  5. Factorise 5m^2 + 20m + 15
    .
  6. Factorise 8p^2 + 4p
    .
  7. Factorise 12x^3 + 6x^2
    .
  8. Factorise 14a^2 + 21a
    .
  9. Factorise 16n + 20n^2
    .
  10. Factorise 24x^2 + 36x
    .

Answers and Explanations

Easy Level Answers

  1. 4x + 8 = 4(x + 2)
    • The common factor is 4. Dividing gives us x + 2
      . Thus, we write it as 4(x + 2)
      .
  2. 3a + 6 = 3(a + 2)
    • The common factor is 3. Dividing gives us a + 2
      . Thus, we write it as 3(a + 2)
      .
  3. 5b + 10 = 5(b + 2)
    • The common factor is 5. Dividing gives us b + 2
      . Thus, we write it as 5(b + 2)
      .
  4. 2m + 4 = 2(m + 2)
    • The common factor is 2. Dividing gives us m + 2
      . Thus, we write it as 2(m + 2)
      .
  5. 7x + 14 = 7(x + 2)
    • The common factor is 7. Dividing gives us x + 2
      . Thus, we write it as 7(x + 2)
      .
  6. 9y + 12 = 3(3y + 4)
    • The common factor is 3. Dividing gives us 3y + 4
      . Thus, we write it as 3(3y + 4)
      .
  7. 10a + 15 = 5(2a + 3)
    • The common factor is 5. Dividing gives us 2a + 3
      . Thus, we write it as 5(2a + 3)
      .
  8. 6x + 3 = 3(2x + 1)
    • The common factor is 3. Dividing gives us 2x + 1
      . Thus, we write it as 3(2x + 1)
      .
  9. 8p + 16 = 8(p + 2)
    • The common factor is 8. Dividing gives us p + 2
      . Thus, we write it as 8(p + 2)
      .
  10. 4z + 20 = 4(z + 5)
  • The common factor is 4. Dividing gives us z + 5
    . Thus, we write it as 4(z + 5)
    .

Medium Level Answers

  1. 12x + 18 = 6(2x + 3)
    • The common factor is 6. Dividing gives us 2x + 3
      . Thus, we write it as 6(2x + 3)
      .
  2. 15b + 10b = 5b(3 + 2)
    • The common factor is 5b. Dividing gives us 3 + 2
      . Thus, we write it as 5b(3 + 2)
      .
  3. 14a + 21 = 7(2a + 3)
    • The common factor is 7. Dividing gives us 2a + 3
      . Thus, we write it as 7(2a + 3)
      .
  4. 8m + 4n = 4(2m + n)
    • The common factor is 4. Dividing gives us 2m + n
      . Thus, we write it as 4(2m + n)
      .
  5. 9x + 27 = 9(x + 3)
    • The common factor is 9. Dividing gives us x + 3
      . Thus, we write it as 9(x + 3)
      .
  6. 6y + 15y = 3y(2 + 5)
    • The common factor is 3y. Dividing gives us 2 + 5
      . Thus, we write it as 3y(2 + 5)
      .
  7. 10p + 25 = 5(2p + 5)
    • The common factor is 5. Dividing gives us 2p + 5
      . Thus, we write it as 5(2p + 5)
      .
  8. 5a + 20b = 5(1a + 4b)
    • The common factor is 5. Dividing gives us 1a + 4b
      . Thus, we write it as 5(1a + 4b)
      .
  9. 4x + 16y = 4(x + 4y)
    • The common factor is 4. Dividing gives us x + 4y
      . Thus, we write it as 4(x + 4y)
      .
  10. 20k + 15 = 5(4k + 3)
    • The common factor is 5. Dividing gives us 4k + 3
      . Thus, we write it as 5(4k + 3)
      .

Hard Level Answers

  1. 4x^2 + 8x = 4x(x + 2)
    • The common factor is 4x. Dividing gives us x + 2
      . Thus, we write it as 4x(x + 2)
      .
  2. 6a^2 + 12a = 6a(a + 2)
    • The common factor is 6a. Dividing gives us a + 2
      . Thus, we write it as 6a(a + 2)
      .
  3. 10x^2 + 15x = 5x(2x + 3)
    • The common factor is 5x. Dividing gives us 2x + 3
      . Thus, we write it as 5x(2x + 3)
      .
  4. 9y^2 + 27y = 9y(y + 3)
    • The common factor is 9y. Dividing gives us y + 3
      . Thus, we write it as 9y(y + 3)
      .
  5. 5m^2 + 20m + 15 = 5(m^2 + 4m + 3)
    • The common factor is 5. Dividing gives us m^2 + 4m + 3
      . Thus, we write it as 5(m^2 + 4m + 3)
      .
  6. 8p^2 + 4p = 4p(2p + 1)
    • The common factor is 4p. Dividing gives us 2p + 1
      . Thus, we write it as 4p(2p + 1)
      .
  7. 12x^3 + 6x^2 = 6x^2(2x + 1)
    • The common factor is 6x². Dividing gives us 2x + 1
      . Thus, we write it as 6x^2(2x + 1)
      .
  8. 14a^2 + 21a = 7a(2a + 3)
    • The common factor is 7a. Dividing gives us 2a + 3
      . Thus, we write it as 7a(2a + 3)
      .
  9. 16n + 20n^2 = 4n(4 + 5n)
    • The common factor is 4n. Dividing gives us 4 + 5n
      . Thus, we write it as 4n(4 + 5n)
      .
  10. 24x^2 + 36x = 12x(2x + 3)
    • The common factor is 12x. Dividing gives us 2x + 3
      . Thus, we write it as 12x(2x + 3)
      .

I hope this helps you understand factorising brackets better! Keep practicing, and soon it will become second nature. If you have any questions, feel free to ask!