Expansion and Factorization of Algebraic Expressions


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Expansion and Factorization of Algebraic Expressions

  1. 1. Page 1 of 4Expansion and Factorization ofAlgebraic ExpressionsBefore we get into what exactly is expansion and factorization, let’s take a closer look at the threedifferent formulas. These three formulas can be applied and used when both expanding andfactoring algebraic expressions.Formula Number OneAlso note the following:Formula Number TwoFormula Number ThreeExpansionExpansion is the act of expanding (obviously), or to literally remove all brackets that are present inan expression, mathematically speaking. Usually, you’ll encounter a few expressions in your mathexams where they place two sets of two terms, both in brackets, side by side, like this:This kind of math question requires you to expand the expression such that the brackets will beremoved in the process, and the entire question can be simplified to its simplest form (which will, ofcourse, be your answer – the simplest form).Copytight©2011- Hubert Lawrence Yeo
  2. 2. Page 2 of 4Now, let me guide you step by step on how to expand different expressions that you may face inyour math exams, and later on, point out the common mistakes that most students make whileattempting to solve these questions.Expand (x +2)(x+3) 1. Separate the terms in the first bracket into two different items (‘x’, and ‘+2’ in this case) 2. Multiply the first item into the second bracket, like this. 3. Next, multiply the second term into the second bracket, like this. 4. Then, add the two sets of terms together, like this. That is method 1 – now let’s look at method two 1. Multiply the two terms in the first bracket into the second bracket, one by one, like this.That’s more or less it – I love to call the method used above the ‘brute force’ method. I won’t touchthe formulas that are given to you above because they are more or less straightforward andpainfully simple – if you got any questions to ask, feel free to email me.NOTE: The formulas given to you above can be used for both factorization and expansion.Common Mistakes This may seem like a rather careless mistake to you but believe it or not, many pupils make this mistake during the examinations, whether or not they are careless or consistent in their work:Note that would give you a POSITIVE six, not a negative one.FactorizationCopytight©2011- Hubert Lawrence Yeo
  3. 3. Page 3 of 4Factorization is basically the complete opposite of expansion – you want to simplify the expressiongiven to you in a sense that it will be less cluttered. Compared to expansion, factorization is, to me,much more difficult. The idea of removing things and spreading them out (expansion) is to me muchmore easier than putting all of them back together in the same position without making anymistakes (factorization). Now, let’s got through the steps shall we?Common Term FactorizationThis method is carried out by observing the different terms (coefficient etc.) in the expression andlooking out for terms that are common and can be factored out. Let me give you a few examples:Factorize 3x+6 1. Check the terms for any common numbers or terms. (In this case, 3 and 6 has a common factor – 3.) 2. Bring the common number/term, or in this case factor, out of the expression, like this.Common Mistakes Factorize Seems simple enough – but many students make a critical error sometimes when writing down their final answer. Let’s see… The answer here is wrong! Many students forget to include the 1 before the 2x^2y. It should be as such:Three Methods of Expansion and FactorizationCopytight©2011- Hubert Lawrence Yeo
  4. 4. Page 4 of 4To find out more about the three different methods of expansion and factorization, you coulddownload and try using the excel application that was created by my math teacher, Mr. Antony Khoo,from the links given below.Expansion:http://dl.dropbox.com/u/33243124/Secondary%20Two%20Math%20Notes%20-%20Revised%20and%20Rewritten/Expansion%202009%20-%20Mr.%20Antony%20Khoo.xlsFactorization:http://dl.dropbox.com/u/33243124/Secondary%20Two%20Math%20Notes%20-%20Revised%20and%20Rewritten/Factorisation%202009%20-%20By%20Mr.%20Antony%20Khoo.xlsDISCLAIMER: The above Microsoft Excel application was developed and made by my math teacher,Mr. Antony Khoo. I have no part in making this application whatsoever and will not accept any formof credit that may be directed to me for the application used – all credit should go to my teacher, Mr.Antony Khoo. I will only accept credit for the writing of the notes.Copytight©2011- Hubert Lawrence Yeo