{"id":244692,"date":"2024-05-13T16:00:54","date_gmt":"2024-05-13T08:00:54","guid":{"rendered":"https:\/\/thepiquelab.com\/blog\/?p=244692"},"modified":"2025-08-11T17:27:15","modified_gmt":"2025-08-11T09:27:15","slug":"algebra-how-to-expand-linear-expressions","status":"publish","type":"post","link":"https:\/\/thepiquelab.com\/blog\/algebra-how-to-expand-linear-expressions\/","title":{"rendered":"Algebra: How To Expand 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

Do you struggle with expanding algebraic linear expressions during your Math examinations?<\/p>\n

Keep on reading for a step-by-step guide to expanding linear expressions, along with some useful tips to make the topic of Algebra easier for you!<\/p>\n

<\/p>\n\n

Let’s Take A Look At This Algebra Question<\/strong><\/span><\/h2>\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. Beginner\u2019s Guide To Cross Multiplication<\/strong><\/a><\/li>\n<\/ol>\n<\/div>\n

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

    First, let us copy the question.<\/p>\n

    \"The<\/p>\n

    \n

    \ud83d\udca1<\/span> What Do The Brackets Mean? <\/span><\/strong>\ud83d\udca1<\/span><\/p>\n

    It means that you are supposed to multiply the number outside the brackets to everything inside the brackets<\/p>\n<\/blockquote>\n

    Therefore, we are going to multiply 2 to -4x and +3<\/span>.<\/p>\n

    \"The<\/p>\n

    Some of you may know this method as the D<\/span>istributive Law<\/span><\/strong>. Some may know this as the Rainbow Method<\/span><\/strong> because the arrows look like a rainbow \ud83c\udf08<\/span><\/p>\n

    \n

    \ud83c\udf08 <\/span>How To Remember The Distributive Law In Algebra<\/strong><\/span> \ud83c\udf08<\/span><\/p>\n

    Think of a rainbow! \ud83c\udf08<\/span><\/p>\n<\/blockquote>\n

    Do you panic just by looking at the algebraic expression above? Don\u2019t worry because I am going to share a trick I have been teaching my students.<\/p>\n

    Look inside the brackets and ask yourself how many terms there are in the equation.<\/p>\n

    \"How<\/p>\n

    There are two terms inside the bracket. These are -4x<\/em> and +3.<\/p>\n

    To help you visualise and differentiate the two terms, you can draw a line between the two.<\/p>\n

    \"How<\/p>\n

    Now, you can start multiplying by drawing arrows \ud83c\udf08<\/p>\n

    The arrow \ud83c\udf08 below signifies multiplication. So let us multiply 2 with -4x<\/em>.<\/p>\n

    <\/p>\n

    \"How<\/p>\n

    That is -8x.<\/p>\n

    Let us move on to the next term and do the same. Draw an arrow \ud83c\udf08 and multiply 2 by +3.<\/p>\n

    \"How<\/p>\n

    The answer is +6.<\/p>\n

    Therefore, our final answer is -8x<\/em> + 6.<\/p>\n

    <\/p>\n

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

    -8<\/span>x<\/span><\/em> + 6<\/span><\/strong><\/p>\n

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

    \"The<\/p>\n

    Again, the brackets mean we need to multiply 3x<\/em> with all of the terms inside the brackets.<\/p>\n

    How many terms are inside the brackets? There are two! Let us draw a line to separate the two terms.\u00a0<\/p>\n

    \"How<\/p>\n

    Next, draw your arrow \ud83c\udf08<\/span>\u00a0and multiply.<\/p>\n

    \"How<\/p>\n

    3x<\/em> x\u00a0x<\/em><\/p>\n

    = 3x<\/em>2<\/sup><\/strong><\/p>\n

    When you are multiplying x<\/em> with x<\/em>, you will get x<\/em>2<\/sup>.<\/p>\n

    If this does not make sense to you, remember that when you are multiplying 11 by 11 in index notation, you will get 112<\/sup>. So the same is true when x<\/em> is multiplied by x<\/em>.<\/p>\n

    \"How<\/p>\n

    Next, let us multiply 3x<\/span> with +5 \ud83c\udf08<\/span><\/p>\n

    \"How<\/p>\n

    We will get 15x<\/em>.<\/p>\n

    Therefore, our final answer is 3x<\/em>2<\/sup>\u00a0+ 15x.<\/em><\/p>\n

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

    3x<\/em>2<\/sup>\u00a0+ 15x<\/em><\/strong><\/p>\n

    <\/p>\n

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

    \"The<\/p>\n

    Apply the same steps that we did in the previous equations. Let us determine the terms that we have inside the bracket.<\/p>\n

    \"How<\/p>\n

    We have 2x<\/em> and -5.<\/p>\n

    Next, let us multiply \ud83c\udf08 them with the number outside the bracket.<\/p>\n

    <\/p>\n

    \"How<\/p>\n

    -7 x 2x<\/em><\/p>\n

    =-14x<\/em><\/p>\n

    \"How<\/p>\n

    For the second term, what is -7 x -5? \ud83c\udf08<\/span><\/p>\n

    \n

    \ud83d\ude32<\/span>\u00a0What Happens<\/strong><\/span> When <\/span>You Multiply Two <\/span>Negative<\/span><\/strong> Numbers?<\/strong> \ud83d\ude32<\/span> <\/span><\/p>\n

    A negative and a negative make a positive.<\/p>\n<\/blockquote>\n

    Therefore, it is +35.<\/p>\n

    Our final answer is -14x<\/em> + 35.<\/p>\n

    <\/p>\n

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

    -14x<\/span> + 35<\/strong><\/p>\n

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

    \"The<\/p>\n

    For some of you, this last algebraic equation might seem strange because there is only a minus sign and no number outside the bracket.<\/p>\n

    \n

    \ud83d\ude80<\/span>\u00a0<\/span>Remember This When <\/span><\/strong>You See A Negative Sign Outside The Bracket<\/strong> \ud83d\ude80<\/span> <\/span><\/p>\n

    Whenever you see algebraic equations like this, remember that there is a hidden 1 and the minus sign represents -1. You can write down 1 after the negative sign so you won\u2019t get confused!<\/p>\n<\/blockquote>\n

    \"How<\/p>\n

    Now, we can proceed with the next steps. Draw a line between the two terms inside the bracket.<\/p>\n

    \"How<\/p>\n

    Next, multiply \ud83c\udf08<\/span>\u00a0the number outside the bracket with the first term. <\/p>\n

    \"How<\/p>\n

    -1 x 7x<\/em><\/p>\n

    = -7x<\/em><\/p>\n

    <\/p>\n

    Next, draw an arrow \ud83c\udf08<\/span> and multiply -1 with -1.<\/p>\n

    \"How<\/p>\n

    -1 x -1 = +1<\/p>\n

    Therefore, the answer is -7x<\/em> + 1.<\/p>\n

    \n

    \ud83e\udd14<\/span>\u00a0Remember This Shortcut When Multiplying Against A Negative Sign<\/strong> \ud83e\udd14<\/span><\/span><\/p>\n

    The negative sign outside will flip all the signs inside the bracket.<\/p>\n<\/blockquote>\n

    <\/p>\n

    \"The<\/p>\n

    Inside the brackets, I have a +7x<\/em> and -1. When the brackets are removed, the minus sign will flip the signs of the terms in the bracket.<\/p>\n

    Therefore, it will be -7x<\/em> + 1.<\/p>\n

    <\/p>\n

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

    -7x<\/span> + 1<\/strong><\/p>\n

    Conclusion<\/span><\/h2>\n

    Looking at algebraic expressions can be overwhelming when you do not know where to start but I hope that this Algebra blog post has served as your guide in understanding how to expand linear expressions.<\/p>\n

    Remember to draw a line between the terms inside the bracket before multiplying each term so you won\u2019t get confused.<\/p>\n

    Stay tuned for more blog posts about Algebra!<\/p>\n

    <\/p>\n

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    In this article, we’ll be discussing how to use the Rainbow Method to solve this Secondary 1 Math Algebra question.<\/p>\n","protected":false},"author":52,"featured_media":244728,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","om_disable_all_campaigns":false,"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"categories":[59,60],"tags":[],"post_folder":[],"modified_by":"Jaimie Aberia","_links":{"self":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/244692"}],"collection":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/users\/52"}],"replies":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/comments?post=244692"}],"version-history":[{"count":28,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/244692\/revisions"}],"predecessor-version":[{"id":246598,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/244692\/revisions\/246598"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media\/244728"}],"wp:attachment":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media?parent=244692"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/categories?post=244692"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/tags?post=244692"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/post_folder?post=244692"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}