Question

An expression is shown below:

6x2y − 3xy − 24xy2 + 12y2

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Answer 1

Given:

The given expression is:

`6x^2y-3xy-24xy^2+12y^2`

To find:

Part A: The expression by factoring out the greatest common factor.

Part B: Factor the entire expression completely.

Solution:

Part A:

We have,

`6x^2y-3xy-24xy^2+12y^2`

Taking out the highest common factor 3y, we get

`=3y(2x^2-x-8xy+4y)`

Therefore, the required expression is
`3y(2x^2-x-8xy+4y)`.

Part B:

From part A, we have,

`3y(2x^2-x-8xy+4y)`

By grouping method, we get

`=3y(x(2x-1)-4y(2x-1))`

`=3y(x-4y)(2x-1)`

Therefore, the required factored form of the given expression is
`3y(x-4y)(2x-1)`.