How,Expand,Brackets,Expanding, education How to Expand Brackets
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Expanding and simplifying brackets is an essential skill for anymathematician, as it is so widely used in different areas of mathematics. Inthis article, I show how brackets can be multiplied out by a variety ofdifferent methods, using the example of (a+b)^2, and also explain thefundamental rules in writing algebraic expressions.Let's look at the example of (a+b)^2. The ^2 bit means "squared",or multiplied by itself. So it is basically just a fancy way of telling us totake two lots of (a+b) and multiply them together:(a+b)(a+b)Expanding brackets means multiplying them together. It is important rememberthis as in the expression shown above, there isn't any sign between thebrackets. Therefore, what we actually mean is(a+b) x (a+b)Similarly, when we multiply a by b, we write just ab to mean a x b. Thereason why in algebra we do not show the multiplication sign is thatmathematicians are lazy, and as multiplication is used so much in algebra, theycan't be bothered to write "x" all the time, and it can also veryeasily be confused with the algebraic letter x, which is used very commonly inalgebra.So, now it's time to expand these brackets. When you multiply out brackets,you have to multiply every term in the first bracket with every term in thesecond bracket. This is shown below:(a+b)(a+b) = a x a + ab +ba + b x bWe can now tidy this up a bit. On the outside, we have a x a and b x b. Wecan write these as a^2 and b^2. This is kind of the opposite of what we didright at the beginning. Also, ab = ba (you can try this with numbers - e.g. 7 x8 = 8 x 7). So we have two lots of ab, which we can rewrite as 2ab. Ourexpansion becomes(a+b)(a+b) = a^2 + 2ab + b^2Excellent! We have successfully expanded (a+b)^2! The first part of theexpansion that got us a x a + ab + ba + b x b may have been a bit hard tofollow, or difficult to remember. There are various ways of remembering how todo this first part of the expansion (not all of them nice) but there are acouple civilised ways of doing it shown below:Method 1: FOILThis is a fun little mnemonic to help you learn how to expand brackets. Itgoes like this:F stands for First - multiply the first term (letter) in each brackettogether.O stands for Outside - multiply the outside two terms together.I stands for Inside - multiply the inside two terms together.L stands for Last - multiply the last two terms in each bracket together.Method 2: Multiplication TablesIf you thought you had rid yourself of those when you'd finally learnt allyou times tables, then you were wrong! Even if you do maths at university levelyou find yourself doing them whilst studying Group Theory. No, you're not donewith them yet. Times tables are for life, not just for junior school. Here wego then...x, a, b a a^2 abb ba b^2Hopefully that didn't bring back too many painful memories. At least now,armed with an understanding of how to write algebraic expressions and expandbrackets by a variety of different methods, you have at your fingertips of themost fundamental skills that gives you the potential to expand yourmathematical knowledge in a variety of different areas! Normal 0 false false false EN-GB X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable{mso-style-name:"Table Normal";mso-tstyle-rowband-size:0;mso-tstyle-colband-size:0;mso-style-noshow:yes;mso-style-priority:99;mso-style-qformat:yes;mso-style-parent:"";mso-padding-alt:0cm 5.4pt 0cm 5.4pt;mso-para-margin-top:0cm;mso-para-margin-right:0cm;mso-para-margin-bottom:10.0pt;mso-para-margin-left:0cm;line-height:115%;mso-pagination:widow-orphan;font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;} Article Tags: Expand Brackets
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