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Question 96388This question is from textbook
: The question in the book is... Simplify the expression by combining like terms.
20. p + 9q + 9 + 14P
24. 8(y + 2)+ y + 4
The book doesn't give examples of the above questions. Please help my daughter to understand combining like terms when ( ) are involved in the expression. Thank you. - Laura P.
This question is from textbook
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The problem tells you to combine like terms. What it doesn't tell you in the instructions is
the definition of "like terms." Like terms contain the exact same variables (letters).
For example: 3a and 2a are like terms because they have the letter "a" in common. 3a and 2 are
not like terms because one has the letter "a" and the other does not have a letter at all.
If a term does not have a letter at all, it is only like another term that does not have a
letter either. For example 3 and 2 are like terms because neither has a letter.
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Starting with this background, let's work problem 20.
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Given:
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p + 9q + 9 + 14p
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(I'm going to assume that when you typed 14P you actually meant 14p. Technically a capital
P could represent something different from a lower case p.)
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Note that there are two like terms ... +p and +14p ... they are like because they both
contain the just the single letter p. Therefore, they can be combined. p + 14p equals 15p.
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So you can now delete p and +14p and replace them with 15p to get:
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15p + 9q + 9
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There are no other combinations that can be done because there are no "like" terms. One
contains a p, one a q, and one has no associated letter.
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Therefore, the answer to this problem is just 15p + 9q + 9
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Now let's go to problem 24. This problem contains a minor "twist." You are given:
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8(y + 2) + y + 4
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The "twist" is that you first have to do the distributed multiplication that is indicated
by the parentheses. What is meant by 8(y + 2)? It means that you multiply 8 times each of
the terms inside the parentheses. So you multiply 8 times y to get +8y and then you multiply
8 times +2 to get +16. So you can replace 8(y + 2) with 8y + 16 and this makes the problem
become:
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8y + 16 + y + 4
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Notice that 8y and +y are "like" terms because they both contain "y." They can be combined
by adding them. 8y + y = 9y. So replace the two terms with 9y and the problem reduces to:
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9y + 16 + 4
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Notice that the terms +16 and + 4 are like terms because neither has a letter. They are both
just numbers so they can be added ... 16 + 4 = 20. So replace the 16 and 4 with their equivalent
20 to make the problem become: 9y + 20
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There are no "like" terms in these two terms ... one term contains a letter and the other
does not. Therefore, no other combining can be done and the answer to this last problem is
just: 9y + 20
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Hope this helps you to understand the problems a little better.
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