Question

An expression is shown below:

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 $3y(x-4y)(2x-1)$.