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Question 65204: 3x-2[y-2(x+3[2x+3y])]
simplify
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website! 3x - 2[y - 2(x + 3[2x + 3y])]
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Look for the first innermost pair of grouping symbols, that is, grouping symbols which contain no grouping symbols. we find the [2x + 3y]. We notice that there is nothing we can do inside of it. We now notice that it has a +3 just before it. So we remove those grouping symbols by using the distributive
principle and we replace the "+ 3[2x + 3y]" by "+ 6x + 9y":
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3x - 2[y - 2(x + 6x + 9y)]
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Now we look for the first innermost pair of grouping symbols, that is, grouping symbols which contain no grouping symbols. we find the [x + 6x + 9y}. We notice that there is something we can do inside of it. We can combine the like terms x and 6x, since x + 6x equals 7x. So we replace the "[x + 6x + 9y]" by "[7x + 9y]:
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3x - 2[y - 2(7x + 9y)]
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Look for the first innermost pair of grouping symbols, that is, grouping symbols which contain no grouping symbols. we find the [7x + 9y]. We notice that there is nothing we can do inside of it. We now notice that it has a "- 2" just before it. So we use the distributive principle and replace the
"- 2(7x + 9y)" by "- 14x - 18y":
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3x - 2[y - 14x - 18y]
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Now we look for the first innermost pair of grouping symbols, that is, grouping symbols which contain no grouping symbols. we find the [y - 14x - 18y}. We notice that there is something we can do inside of it. We can combine the like terms y and "- 18y", since y - 18y equals -17y. So we replace [y - 14x - 18y] by "[-14x - 17y]:
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3x - 2[-14x - 17y]
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Look for the first innermost pair of grouping symbols, that is, grouping symbols which contain no grouping symbols. we find the [-14x - 17y]. We notice that there is nothing we can do inside of it. We now notice that it has a "- 2" just before it. So we use the distributive principle and replace the
"- 2(- 14x - 18y] by "+ 14z + 34y":
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3x + 28x + 34y
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Now when we look for the innermost pair of grouping symbols, we find none. So we look for terms to combine. We replace the 3x + 28x by 31x and we have
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31x + 34y.
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Nthing else can be done so that is the answer in the simplest form.
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Edwin
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