ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Algebra- Expanding and simplifying equations

Updated on October 4, 2010

Expanding and Simplifying Algebraic Equations

 

Here we are going to take a look at how to expand and simplify Algebraic Equations;

Example 1

 

When multiplying out two brackets make sure that each term in the second bracket is multiplied by each term in the first bracket.

See examples below, I've colour coded the steps of the equations to make them simpler to understand.

 

An easy way to multiply out two brackets is to use the grid method shown below;

Grid method for (x  +  3) ( x  +  4)

 

Example 2

 

Again multiply all the terms in the second bracket by the terms in the first bracket

 

 

The grid method for (2x  -  4) (x  -  5)

 

Example 3

 

Again we'll multiply all the terms in the second bracket by the terms in the first bracket;

 

In this equation (4x-  3) ( 3x  +  1)

 as there are no like terms to gather we just write out the expanded expression;

 

12x3  +  4x2  -  9x  -  3

 

 The grid method for (4x-  3) (3x  +  1)

Comments

    0 of 8192 characters used
    Post Comment

    • t.elia profile image
      Author

      t.elia 4 years ago from Northern Ireland

    • profile image

      Step 6 years ago

      I need to find an equation that relates to 1 & 2, 2 & 8, 3 & 18, and 4 & 32

    • profile image

      unknown 6 years ago

      how do i simplify and expand 2(x+5)(x-2)

    • profile image

      nice 6 years ago

      (X-3/2Y)^5 pls! expand. thank you

    • t.elia profile image
      Author

      t.elia 6 years ago from Northern Ireland

      Hi Cazza

      9xy(5x + 6y)

      9 x 5 = 45

      X x X = X^2

      y

      +

      9 x 6 = 54

      X

      Y x Y = Y^2

      Regroup this as 45X^2Y + 54XY^2 (Ans)

      Hope this helps

    • profile image

      Cazza 6 years ago

      I need to work out 9xy(5x+6y)I have no idea what to do can you help me and fast please. Thanks

    • t.elia profile image
      Author

      t.elia 6 years ago from Northern Ireland

      Academysigma,

      Thanks that is no problem glad you found it useful.

      Telia

    • academysigma profile image

      academysigma 6 years ago from Hong Kong

      Hi T.Elia - thanks for this, I've linked to this hub from one of mine, I hope you're ok with that. If not, pls. let me know.

    • t.elia profile image
      Author

      t.elia 6 years ago from Northern Ireland

      HELPPP

      You are multiplying out the brackets here;

      p^2(2p - 1)

      p^2 x p = p^3 ( to multiply these you add them)

      Then multiply out your 2

      and finally do the last part of this equation;

      p^2 x 1 = p^2

      The answer now looks like this

      2p^3 - p^2 (Ans)

      Good Luck

    • profile image

      helpppp 6 years ago

      p^2(2p-1)

    • profile image

      Jelly 7 years ago

      Wow! This helped me a lot, thanks for making it seem so simplse! :)

    • profile image

      meee 7 years ago

      what do all these letters mean?!?

    • t.elia profile image
      Author

      t.elia 7 years ago from Northern Ireland

      Hi secret.

      Thankyou for being brave enough to write in.

      At the moment in school you are learning to expand the brackets, therefore

      5x (x - 2 )

      5x multiplied by x = 5x^2

      5x multiplied by -2 = -10x

      = 5x^2 - 10x (this is the answer)

      5x squared - 10x

    • profile image

      secret 7 years ago

      Im learning this in school but my sums are like this

      5x(x-2)?

      =7x? i don't know? helllp

    • t.elia profile image
      Author

      t.elia 7 years ago from Northern Ireland

      Thanks Bk Creative... I find that I have achieved what I set out to do in this tutorial via your comments. My daughter has dyslexia and dyspraxia, as a result I found writing in black didn't achieve anything so I used this principle, I found that it helped immensely especially when colour coded and written out in steps form.

      She is now at Uni doing a degree in Sport Science and this year they have given her a reader for her exams.

      Prior due to lack of funding she didn't receive any help other than my own.

      My daughters classmates found this method extremely helpful as well because they could visually see the process they had to follow to attain the answer.

      Many thanks for your wonderful comments.

      Looking forward to reading your hub on the "golden ratio"

    • BkCreative profile image

      BkCreative 7 years ago from Brooklyn, New York City

      Good grief - this is soooo clear! I tutor students sometimes and there is absolutely nothing clear that I can show them when it comes to simplifying - until now. Wow! So of course I can bookmark and use this. Whew! The colors, the arrows, it all helps tremendously.

      Oh, I never got around to writing about the golden ratio - but maybe I will now because it is a shape we are so familiar with - like our credit cards, and driver licenses and so much more. Glad you mentioned that.

      Great to find clear math - whew!

      Rated up and more.

    • t.elia profile image
      Author

      t.elia 7 years ago from Northern Ireland

      Thankyou for your positive comment carolina muscle, it makes the effort to show the workings out of maths worthwhile.

    • carolina muscle profile image

      carolina muscle 7 years ago from Charlotte, North Carolina

      You make this seem a lot simpler !!! Thanks!

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: "https://hubpages.com/privacy-policy#gdpr"

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)