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Combining Algebra Like Terms
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Combining Algebra Like Terms



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Combining Algebra Like Terms Combining Algebra Like Terms Presentation Transcript

  • Image Source: http://3.bp.blogspot.com
  • People who are twins are a “like pair” becausethey have the exact same features.An Algebra Equation we can write for this is : T + T = 2T Eg. One Twin + One Twin = 2 Twins.In Algebra we call this “Combining Like Terms”.
  • A typical question is : Simplify 2a + 3b + 3a 2a + 3b + 3aIf we think of “a” being Apples and “b” being Bananas,then we have the following situation: We can see that by combining the like objects, the above can be simplified to be 5 Apples and 3 Bananas, which in Algebra is: 5a + 3b Images from Clker.com View slide
  • "Like Terms" are terms that contain the same letter Variables which are raised to the exact same Powers.( Only the first number "Coefficients" of the terms are different ) 3a and 2a are like terms, because although they have different coefficient numbers, they have the exact same letter "a" in them. Some other examples of like terms are: 3d2y 12d2y - 2d2y d2y bh 4bh -5bh -bh View slide
  • Always remember that the Powers need to be the same. P3 and P2 are NOT like termsThey have the same Variable letter “P” in them, but theirExponent Index values are different. Just as the Playstation PS-3 is different to the PS-2, P3 is also different to P2 . The items are not identical.
  • Just like checking two cars very carefully, make sure youcheck every part of each pair of Algebraic Terms. 2 3 3 2 5 3 2x y z and 3x y z
  • Decide if the terms in each pair of items are “Like Terms”.1) 4g and 4h ______2) 3h and –h ______3) 5x and 4xy ______4) 2x2y3 and 2x2y5 ______5) 5p2q3 and -4p2q3 ______
  • Decide if the terms in each pair of items are “Like Terms”.1) 4g and 4h NO – letter variables are different.2) 3h and –h YES – letters the same ( –h = -1h)3) 5x and 4xy NO – letter variables are different.4) 2x2y3 and 2x2y5 NO – y powers are different.5) 5p2q3 and -4p2q3 YES – letters & powers same
  • Often in real life it is necessary to combine like itemstogether to create a shorter list of items we can deal with.For example, imagine that a mathematics class is on anexcursion and need to order a take away food lunch.It would be crazy to read out each individual order, one aftereach other, at the counter of the fast food restaurant.Instead we would total up how many burgers, how manyfries, how many drinks, etc that we need to order for thewhole group. We combine the items into a summarised list.This type of summarizing process is exactly the sameas combining Algebraic Like Terms.
  • To Combine Like Terms, we add together items that are thesame to make a simplified shorter list of items.Consider the following family take-away order: + + + + +We can write this in Algebra as: 2b + f + d + 3b + 2f + 2dIf we combine like items, we get a simplified list as follows:5b + 3f + 3d Images from Clker.com
  • We can also Subtract Like TermsSuppose that we have bought 5 apples and 6 bananas, butwe eat two bananas before putting our fruit into the bowl. + -The Algebra is: 5a + 6b – 2b = 5a + 6b – 2b (6 bananas take away 2 is 4) = 5a + 4b = 5a + 4b Images from Clker.com
  • WARNING: Like Terms are only used forAdding and Subtracting algebraic terms.We never use combining like terms for Multiplying and Dividing ! Images from Clker.com
  • To Combine Like Terms, follow these steps: Identify the items which are “Like Terms” Rewrite the expression so that the like terms are all next to each other Combine the groups of like terms together to make a simplified shorter final answer This last step involves adding or subtracting the like terms
  • Simplify: 7mn – 2mn + 3mn7mn – 2mn + 3mn (three like terms)= 5mn + 3mn= 8mn= 8mn
  • Simplify : 4g + 3h + 2g + 3gh + 6hg 4g + 3h + 2g + 3gh + 6gh ( 6hg = 6gh ) = 4g + 2g + 3h + 3gh + 6gh = 6g + 3h + 9gh = 6g + 3h + 9gh
  • Simplify the expression: 4w + 3 + 2w - 1 4w + 3 + 2w – 1 (Now Group Like Terms) = 4w + 2w + 3 – 1 (Combine Like Terms) = 6w + 2 = 6w + 2
  • Simplify: 2a – 10ab + 3a – ab – 7 3 2 3 2 2a3 – 10ab2 + 3a3 – ab2 – 7 = 2a + 3a – 10ab – 1ab – 7 3 3 2 2= 5a 3 – 11ab 2 –7= 5a3 – 11ab2 – 7
  • Simplify the expression: 4a2 + 3a + 5a3 - 1 The expression contains terms that are all different from each other. The expression cannot be simplified any further. 2 3 4a + 3a + 5a - 1
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