ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Math Hints: Algebra -- Difference of Squares

Updated on September 22, 2014

Factoring Trick

Algebra students often have to factor polynomials on their exams. Since tests are generally timed, most students would welcome anything that would save them time.

One thing that can make a test quicker is "Difference of Squares". If you can master this concept, you can save yourself a lot of time on standardized math test.

The Difference of Squares: What does it mean?

The Difference of Squares is an interesting mathematical anomaly. In most cases, when you take two binomials (that is an equation of two different bases, as in one being a constant and the other being a variable and adding them together -- for example (2x+7) or (x-5) or even (3x+4y)) that have the same bases (for example (2x+7) times (4x-5) or (y-5) times (y+3) or even (2x+y) times (x-3y)) you end up with a trinomial (that is a three base answer -- for example (8x [squared] +18x-35) or (y [squared] -2y-15) or 2x [squared] -5xy-3y [squared]) respectively.

The picture here shows this concept in its most basic form (x and y can each be any number, variable or combination of number and variable that is a perfect square, like 4, 9, 16, x [squared], 16x [to the 4th power], etc.)

An Example:

In the picture here, since 49 and 36 are perfect squares (49 being 7 [squared] and 36 being 6 [squared]), this works with this equation pictured here.

Why does it work this way?

Notice what happens if you multiply (7x-6) and (7x+6) -- from right to left -- (+6) times (-6) equals (-36), (+6) times (7x) equals (+42x), (-6) times (7x) equals (-42x), (7x) times (7x) equals (49x [squared]) {see the middle section on the picture}.

If you notice, the middle products ( (+42x) and (-42x) ) will cancel each other out {see the line through them} because (+42x) + (-42x) = 0.

The ultimate product {see the bottom line in the picture} ends up being (7x) [squared] {which is 49x [squared]} minus 6 [squared] {which is 36}.

So, you can apply this to factoring -- if you see a set up that is (x+y) times (x-y) you know the answer will be (x [squared] - y [squared]) (see the picture above). And, if you see a set up of (x [squared] - y [squared]), then you know it factors out to (x+y) times (x-y).

Note: this will NOT work with (x [squared] + y [squared]) -- it only works with (x [squared] - y [squared]) -- this is it only works with a difference of squares, not a sum of squares.

Spoonflower is a source for original fabric designs. Please check out our shop.
Spoonflower is a source for original fabric designs. Please check out our shop. | Source

Compugraph Designs' Spoonflower Shop

Buy your fabrics on Spoonflower

If you sew, Spoonflower is a great place to find unusual fabric patterns and designs.

Did this help you understand "difference of squares"?

    0 of 8192 characters used
    Post Comment

    No comments yet.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, 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:

    Show Details
    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 or domains, for performance and efficiency reasons. (Privacy Policy)
    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)
    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.
    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)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)