What are Like Terms?
Date: 11/20/2001 at 23:06:30 From: Carlos Mena Subject: I really need help. Hi, I'm a student at Herbert Hoover Middle School and in math we are doing a project. What are like terms?
Date: 11/21/2001 at 11:15:57 From: Doctor Ian Subject: Re: I really need help. Hi Carlos, A 'term' is the product of some constants (numbers whose values we know) and variables (numbers whose values we don't know). For example, 3 3x 3x^2 3xy^2 3xy^2z^3 are all 'terms'. (Another word for 'term' is 'monomial'. If you add a bunch of monomials together, you get a polynomial.) Two terms are 'like terms' (or 'alike' terms, which in many contexts seems clearer) if their variable patterns are the same. Here is a test you can do: arrange all the variables in alphabetical order, and see if you have any mismatches: 3 x 5 x - | +------------> These patterns match, so these are like terms. 3 x 2 * pi * x - | +-----> These patterns match, so these are like terms. 3 x 3 y - | +------------> These have different variables, so they are NOT like terms. 3 x 3 x y - | +----------> These have different variables, so they are NOT like terms. 3 x^2 y^2 3 x y^2 --- | +-----------> These have the same variables, but different exponents for x, so they are NOT like terms. Note that the 'nomial' in monomial/polynomial means 'name', so the 'name' of a term is the pattern of variables that it contains. Actually, the variables are kind of like last names, and the constants - also called 'coefficients' - are like first names. This isn't an exact analogy: We would say that'John Smith' and 'Joe Smith' are similar names, but we would also say that 'John Smith' and 'John Jones' are similar. However, when talking about terms, we only pay attention to the last names: First name -- 3 xy^2z Same first names, same last names: 'equal' 3 xy^2z ----- Last name First name -- 3 xy^2z Different first names, same last names: 'like' 21 xy^2z ----- Last name First name -- 3 xy^2z Same first names, different last names: 'NOT like' 3 x^2yz ----- Last name Does this help? Write back if you'd like to talk more about this or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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