{"id":244772,"date":"2024-06-03T16:00:18","date_gmt":"2024-06-03T08:00:18","guid":{"rendered":"https:\/\/thepiquelab.com\/blog\/?p=244772"},"modified":"2025-08-11T17:29:09","modified_gmt":"2025-08-11T09:29:09","slug":"algebra-a-step-by-step-guide-to-factorising-linear-expressions","status":"publish","type":"post","link":"https:\/\/thepiquelab.com\/blog\/algebra-a-step-by-step-guide-to-factorising-linear-expressions\/","title":{"rendered":"Algebra: A Step-By-Step Guide To Factorising Linear Expressions"},"content":{"rendered":"

[et_pb_section fb_built=”1″ _builder_version=”4.16″ global_colors_info=”{}”][et_pb_row _builder_version=”4.21.0″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.16″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text _builder_version=”4.21.0″ text_font=”||||||||” hover_enabled=”0″ z_index_tablet=”500″ custom_css_main_element=”sub,||sup {||font-size: 75%;||line-height: 0;||position: relative;||vertical-align: baseline;||}||sup {||top: -0.5em;||}||sub {||bottom: -0.25em;||}” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n

Introduction<\/strong><\/p>\n

Are you wondering why you are not awarded any marks when asked to factorise an algebraic linear equation despite following the steps you learned in school?<\/p>\n

You might be doing an important step wrong!<\/p>\n

In this blog post, I will be sharing a step-by-step guide to factorising linear expressions to help you get full marks in your Algebra questions.<\/p>\n

<\/p>\n\n

How Are Algebraic <\/span>Expansion<\/span> And Algebraic <\/span>Factorisation<\/span> Related?<\/span><\/h2>\n

In the previous blog post<\/a>, we talked about expanding linear expressions.<\/p>\n

If you haven\u2019t read that, click the link<\/a> and go over it first because algebraic expansion and algebraic factorisation are related.<\/p>\n

To give you a brief recap, this is what happens when you expand linear expressions.<\/p>\n

\"The<\/p>\n

Meanwhile, when you are asked to factorise an algebraic expression, you are supposed to go in the opposite direction.<\/p>\n

This time, from 2x<\/em> + 6, you are supposed to take the highest common factor (HCF) and put it outside the bracket so you will get 2(x<\/em> + 3).<\/p>\n

If this looks confusing, keep on reading because I will explain this in detail.<\/p>\n

Let’s Take A Look At This Algebra Question<\/span><\/h2>\n

<\/p>\n

<\/p>\n

\"The<\/p>\n

\n

Read Also:<\/h3>\n
    \n
  1. [Secondary 2 Math Explainer Video] Direct Proportion: Finding The Relationship Between A & H<\/b><\/a><\/li>\n
  2. Algebra: How To Expand Linear Expressions<\/strong><\/a><\/li>\n<\/ol>\n<\/div>\n

    Let\u2019s Solve Part (A)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    The first step in factorising an algebraic expression is to find the highest common factor (HCF).<\/p>\n

    <\/p>\n

    \n

    \ud83e\udd14<\/span>\u00a0What Is HCF?<\/strong> \ud83e\udd14<\/span> <\/span><\/p>\n

    HCF is the largest number that can divide given numbers without leaving a remainder.<\/span><\/p>\n<\/blockquote>\n

    Some of you might think that 5 is the HCF because it can divide 15 and 30. So let us try that.<\/p>\n

    Let us put 5 outside the bracket. What will give you 15x<\/em>?<\/p>\n

    5(3x<\/em>)<\/p>\n

    Next, with 5 outside the bracket, what will give you 30?<\/p>\n

    5(6)<\/p>\n

    Now, let us take all the numbers inside the bracket.<\/p>\n

    =5(3x<\/em> + 6)<\/strong><\/p>\n

    If this is your answer, then I can guarantee that you will get zero marks because this is incorrect<\/strong>!<\/p>\n

    The correct way to do it is to copy the question and write down the HCF.<\/p>\n

    15x<\/em> + 30<\/p>\n

    What is the HCF of 15 and 30? It is 15<\/strong>!<\/p>\n

    So let us put 15 outside the bracket. What will give you 15x<\/em>?<\/p>\n

    15(x<\/em>)<\/p>\n

    Next, with 15 outside the bracket, what will give you 30?<\/p>\n

    15(2)<\/p>\n

    Now, let us take all the numbers inside the bracket.<\/p>\n

    =15(x<\/em> + 2)<\/p>\n

    Therefore, the correct answer is 15(x<\/em> +2).<\/p>\n

    <\/p>\n

    Suggested Answer For Part (A)<\/span>
    <\/h2>\n

    15(x<\/span> +2)
    <\/p>\n

    Let\u2019s Solve Part (B)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    Some of you might be panicking because you don\u2019t see any numbers in this algebraic equation. Don\u2019t worry because I am going to show you how to tackle this question!<\/p>\n

    What do p<\/em>2<\/sup> and pq<\/em>2 <\/sup>mean?<\/p>\n

    Let\u2019s recall, how do you write 11 x 11 in a short form?<\/p>\n

    You will write 112<\/sup>. Why? Because there are two 11s.<\/p>\n

    Similarly, if you have p<\/em> x p<\/em>, it will become p<\/em>2<\/sup> . If it is a q<\/em> x q<\/em>, it will become q<\/em>2<\/sup>.<\/p>\n

    \"The<\/p>\n

    So, what is the HCF of\u00a0 p<\/em>2<\/sup> +\u00a0pq<\/em>2<\/sup>?<\/p>\n

    It is p<\/strong><\/em>! Because after you have taken out p<\/em>, there is nothing else that p<\/em> and q<\/em>2<\/sup> have in common.<\/p>\n

    Now, let us put p<\/em> outside the bracket. What will give you p<\/em>2<\/sup>?<\/p>\n

    p<\/em>(p<\/em>)<\/p>\n

    Next, put p<\/em> outside the bracket, what will give you pq<\/em>2<\/sup>?<\/p>\n

    p<\/em>(q<\/em>2<\/sup>)<\/p>\n

    Now, let us take all the numbers inside the bracket.<\/p>\n

    = p<\/em>(p<\/em> + q<\/em>2<\/sup>)<\/p>\n

    Suggested Answer For Part (B)<\/span>
    <\/h2>\n

    <\/p>\n

    <\/h2>\n

    p<\/em>(p<\/em> + q<\/em>2<\/sup>)<\/p>\n

    <\/p>\n

    Let\u2019s Solve Part (C)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    First, we have to find the HCF of:<\/p>\n