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The Number of Terms in an Expression

Date: 07/12/2006 at 21:31:23
From: michele
Subject: Finding the number of terms in an expression

My text book says 4x + 4y + 4z is three terms, but 4(x + y + z) is
only one term.  

I thought the rule that terms are separated by + or - would apply if 
after multiplying you still had terms separated by + or -.  Other than
somehow combining these unlike terms, what would cause this to become
one term?

I understand that 4xyz would be one term because it's all multiplied, 
not separated by + or -, but why would 4(x + y + z) be one term
instead of three?

Date: 07/12/2006 at 23:31:38
From: Doctor Peterson
Subject: Re: Finding the number of terms in an expression

Hi, Michelle.

Terms are things that are added.  In splitting an expression into
terms, we look only at the "top level"--the last step in the order of 
operations.  So we see 4x + 4y + 4z as a sum of three products,

  (4x) + (4y) + (4z)

The two additions are the last thing done.


  4(x + y + z)

the parentheses force you to do the additions FIRST, and the last
operation done is the multiplication.  That means there is no final
addition step, and the whole thing is thought of as one term, which is
formed as a product just as 4x is.  We don't look inside the 
parentheses to see if there is any addition in there; we think of the
whole parenthesized part just as one chunk that is being multiplied.


- Doctor Peterson, The Math Forum
Associated Topics:
High School Polynomials

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