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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)


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    • t.elia profile imageAUTHOR


      7 years ago from Northern Ireland

    • profile image


      9 years ago

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

    • profile image


      9 years ago

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

    • profile image


      9 years ago

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

    • t.elia profile imageAUTHOR


      9 years ago from Northern Ireland

      Hi Cazza

      9xy(5x + 6y)

      9 x 5 = 45

      X x X = X^2



      9 x 6 = 54


      Y x Y = Y^2

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

      Hope this helps

    • profile image


      9 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 imageAUTHOR


      9 years ago from Northern Ireland


      Thanks that is no problem glad you found it useful.


    • academysigma profile image


      9 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 imageAUTHOR


      9 years ago from Northern Ireland


      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


      9 years ago


    • profile image


      10 years ago

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

    • profile image


      10 years ago

      what do all these letters mean?!?

    • t.elia profile imageAUTHOR


      10 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


      10 years ago

      Im learning this in school but my sums are like this


      =7x? i don't know? helllp

    • t.elia profile imageAUTHOR


      10 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


      10 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 imageAUTHOR


      11 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 

      11 years ago from Charlotte, North Carolina

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


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