# How to distinguish between different meanings of "algebra"

May 29th, 2015
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For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. Such a situation, where a single word has many meanings in the same area of mathematics, may be confusing.

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Factoring in AlgebraFactorsNumbers have factors:And expressions (likex2+4x+3) also have factors:Factorising is the process offinding the factors:Factoring: Finding what to multiply together to get an expression.It is like "splitting" an expression into a multiplication of simpler expressions.Example: factor2y+6Both 2y and 6 have a common factor of 2:2y is 2 y6 is 2 3So you can factor the whole expression into:2y+6 = 2(y+3)So, 2y+6 has been "factored into" 2 and y+3Factoring is also the opposite ofExpanding:Common FactorIn the previous example we saw that 2y and 6 had a common factor of2But to do the job properly make sure you have thehighest common factor, including any variablesExample: factor3y2+12yFirstly, 3 and 12 have a common factor of3.So you could have:3y2+12y = 3(y2+4y)But we can do better!3y2and12yalso share the variabley.Together that makes3y:3y2is 3y y12y is 3y 4So you can factor the whole expression into:3y2+12y = 3y(y+4)Check:3y(y+4) = 3y y + 3y 4 = 3y2+12yAdvicesThe factored form is usually best.When trying to factor, follow these steps:"Factor out" any common termsSee if it fits any of the identities, plus any more you may knowKeep going till you can't factor any moreRemember these IdentitiesHere is a list of common "Identities" (including the"difference of squares"used above).It is worth remembering these, as they can make factoring easier.a2-

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