Question

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

Answer 1

See a solution process below:

Explanation:

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

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

Explanation:

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.