SOLUTION: Factor Completely 12x^3-3xy^2

Question 94206: Factor Completely 12x^3-3xy^2
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
12x^3 - 3xy^2
.
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.
.
So let's factor out 3x from both terms to get:
.
3x(4x^2 - y^2)
.
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].
.
This makes it fall under the factoring rule for the difference of two squares. This rule
says that:
.
(A^2 - B^2) = (A - B)(A + B)
.
(You can multiply out the right side of this rule and it will help you to see why this
rule is true.)
.
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)
.
Putting this result together with the 3x we factored out earlier makes the factored
result:
.
3x(2x - y)(2x + y)
.
and that's the answer to your problem.
.
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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