Lisette L.

asked • 12/28/14

Is this equation correct? If yes,what will be the steps to get the answer?

2x (3x+2y) + 2x (3x-3y)

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Pamela M. answered • 12/28/14

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2x (3x+2y) + 2x (3x-3y) - Original problem
 
First, the hard way: 
2x(3x)+2x(2y) + 2x(3x)-2x(3y) (Step 1 - distribute) (see Note 1) 
6x2+4xy + 6x2-6xy
 
6x2+6x2+4xy-6xy (Step 2 - combine like terms) (see Note 1)
12x2-2xy
 
(2x)(6x)-2x(y) (Step 3 - factor) (see Note 1)
2x(6x-y)
 
Note 1:  usually you don't need to show this step, but I'm showing it for clarification
 
Now, the easy way:
2x (3x+2y) + 2x (3x-3y) - Original problem
2x (3x+2y+3x-3y)
2x (6x-y)
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Lisette L.

Thank you for answering my question and we came up with the same answer except that I didn't reduce. Used the hard way and stopped 12x²-2xy  hehehe 

The story behind asking this question was I asked my co-workers (2 HS Seniors) if they know the Basic Rules in Algebra. Confidently showed me what they are :) So, I gave them this exact problem and both were so sure that there's no way they can solve that problem because of different variable x and y.. Like 2x(3y) and 2x(2y).. They said that I can't multiply it that way. No matter how I insist that it is possible and even told them how it should be done, they argue that I can't do that hehehe Though, at the back of my head, I knew I was right (from what I remember in my HS and College days), I just stop the argument and for some reason, they made me feel that I might be wrong. So, I want to be sure of myself, I found your website and asked the question and was so happy that I was right and maybe can teach those 2 girls more Basic Algebra ;) Or, might as well give them this website and learn more from it hehehe Thank You, Pamela and God Bless!! 
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12/28/14

Lisette L.

By the way, is the same as Distributive Property? 
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12/28/14

Lisette L.

Thank You :) 
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12/28/14

Mary Ann F. answered • 12/28/14

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Happy Sunday Lisette - what are your instructions? Does it say "simplify"? From what you've written, that's all we can do, because you don't have an equation. There is no equals sign. We can't solve for either x or y. 
 
To simplify, we need to distribute the factor from the outside of the parentheses and collect like terms. Multiply the first 2x through the first parenthesis by the 3x and the 2y.... then multiply the second 2x through the second parenthesis by 3x and also by the -3y.
 
(6x2 + 4xy) + (6x2 - 6xy)
 
now collect like terms: 12 x2 - 2xy
we could factor this if we wanted to: 2x(6x -y)
 
OR, is this the expression you came up with to answer a word problem that described a relationship? IF that's the case you'll have to give us the problem description. 
 
 
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Lisette L.

Thank you for answering my question and we came up with the same answer except that I didn't reduce or collect the like terms so I came up with 12x²-2xy hehehe

The story behind asking this question was I asked my co-workers (2 Seniors) if they know the Basin Rules in Algebra. Confidently showed me what they are :) So, I gave them this exact problem and both were so sure that there's no way they can solve that problem because of different variable x and y.. Like 2x(3y) and 2x(2y).. They said that I can't multiply it that way. No matter how I insist that it is possible and even told them how it should be done, they argue that I can't do that hehehe Though, at the back of my head, I knew I was right (from what I remember in my HS and College days), I just stop the argument and for some reason, they made me feel that I might be wrong. So, I want to be sure of myself, I found your website and asked the question and was so happy that I was right and maybe can teach those 2 girls more Basic Algebra ;) Or, might as well give them this website and learn more from it hehehe Thank You, Mary Ann and God Bless!!
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12/28/14

Lisette L.

By the way, is the same as Distributive Property?
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12/28/14

Mary Ann F.

If you're asking how to move from 12x2 - 2xy to 2x(6x - y) that's called factoring. It is essentially distribution in reverse. I realized that there was a common factor of 2x in both terms of 12x2 and 2xy, so I moved it to the outside of the parenthesis, and left the remaining factors inside .
 
When we distribute we multiply a factor by all the members of an expression in parentheses. When we factor we take a common factor OUT of all the terms in the parentheses to the outside. These two are forward and reverse of the same relationship.
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12/28/14

Lisette L.

Thank You, Ms. Mary Ann for refreshing my memory on those Algebra Rules :) And yah, it's simplified instead of calling it an equation.. Thank you again :) 
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12/28/14

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