How do you factor #3xy^2 - 12x#?

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Answer 1 · 2018-03-07T08:38:23

See a solution process below:

First, we can find the Greatest Common Factor of each term:

#3xy^2 = 3 xx x xx y^2#

#3xy^2 = 3 xx 4 xx x#

The common factors are:

#3xy^2 = color(red)(3) xx color(red)(x) xx y^2#

#3xy^2 = color(red)(3) xx 4 xx color(red)(x)#

For a GCF of:

#GCF = color(red)(3) xx color(red)(x) = 3x#

We can rewrite the express and then factor it as:

#(3x * y^2) - (3x * 4) => 3x(y^2 - 4)#

Answer 2 · 2018-03-07T08:39:39

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

We are given: #3xy^2-12x#.

First, take out the greatest common factor of both numbers, that is #3x#.

So, we get

#3x(y^2-4)#

#=3x(y^2-2^2)#

Know that, #a^2-b^2=(a-b)(a+b)#.

We can now let #a=y,b=2#, and so the expression becomes

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

From here, we cannot simplify this further, and therefore this is the final answer.