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. In 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. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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