In the following expression collect like terms: [tex]$13 p^2+5-4 p+7-10 p^2+6 p-9$[/tex]
Answer (2)
The expression 13 p 2 + 5 − 4 p + 7 − 10 p 2 + 6 p − 9 can be simplified by collecting like terms. The combined and simplified result is 3 p 2 + 2 p + 3 . Overall, the final expression is 3 p 2 + 2 p + 3 .
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Group like terms: ( 13 p 2 − 10 p 2 ) + ( − 4 p + 6 p ) + ( 5 + 7 − 9 ) .
Combine coefficients: ( 13 − 10 ) p 2 + ( − 4 + 6 ) p + ( 5 + 7 − 9 ) .
Simplify: 3 p 2 + 2 p + 3 .
The simplified expression is 3 p 2 + 2 p + 3 .
Explanation
Understanding the Problem We are given the expression 13 p 2 + 5 − 4 p + 7 − 10 p 2 + 6 p − 9 and our goal is to simplify it by collecting like terms. Like terms are terms that have the same variable raised to the same power.
Identifying Like Terms First, let's identify the like terms. We have terms with p 2 , terms with p , and constant terms (numbers).
Grouping Like Terms Now, let's group the like terms together:
( 13 p 2 − 10 p 2 ) + ( − 4 p + 6 p ) + ( 5 + 7 − 9 )
Combining Coefficients Next, we combine the coefficients of the like terms:
( 13 − 10 ) p 2 + ( − 4 + 6 ) p + ( 5 + 7 − 9 )
Simplifying the Expression Finally, we simplify the expression:
3 p 2 + 2 p + 3
So, the simplified expression is 3 p 2 + 2 p + 3 .
Examples
Collecting like terms is a fundamental skill in algebra. Imagine you are managing inventory for a store. You might have different quantities of the same item in different locations. Collecting like terms would be like adding up all the quantities of the same item to get a total count. For example, if you have 13 of an item in one location and -10 of the same item (perhaps returns) in another, collecting these like terms would tell you that you have a net total of 3 of that item.
