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Question 94206: Factor Completely 12x^3-3xy^2
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
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12x^3 - 3xy^2
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First you can look for common factors in the two terms. Notice 3 is a common factor because
it is a factor of 3 in the second term and a factor of 12 in the first term. The same can
be said of x. It is a factor of x in the second term and a factor of x^3 in the first term.
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So let's factor out 3x from both terms to get:
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3x(4x^2 - y^2)
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Now notice that the expression in the parentheses is the difference of two squares. That
is, it can be written as [(2x)^2 - (y)^2].
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This makes it fall under the factoring rule for the difference of two squares. This rule
says that:
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(A^2 - B^2) = (A - B)(A + B)
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(You can multiply out the right side of this rule and it will help you to see why this
rule is true.)
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Comparing the left side of the rule to the terms you have in the brackets you can see
that A = 2x and B = y. So you can substitute 2x for every A on the right side of the rule
and y for every B. When you do that you get that [(2x)^2 - (y)^2] factors into (2x - y)(2x +y)
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Putting this result together with the 3x we factored out earlier makes the factored
result:
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3x(2x - y)(2x + y)
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and that's the answer to your problem.
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Hope this helps you to see a way to go about factoring this problem and to get you familiar
with the factoring rule for the difference between two squares.
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