Question

factor the gcf: 6x^4y^3*21x^y^2-9x^2y

Answer 1

Answer:

GCF is $9x^2y$

Step-by-step explanation:

When the GCF or the greatest common factor of the expression is required to be found, then take the common terms, and write the expression in the factor form first.

Now, here we have to find the factor of the expression:

$6x^4y^3\cdot 21x^2y^2-9x^2y$

which can be re-written as:

$6x^4y^3\cdot 21x^2y^2-9x^2y\\=126x^6y^5-9x^2y$

Now, this is further written as:

$126x^6y^5-9x^2y\\=14\cdot \:9x^2x^4yy^4-9x^2y$

Here taking the term $9x^2y$ common, we will get:

$14\cdot \:9x^2x^4yy^4-9x^2y\\=9x^2y\left(14x^4y^4-1\right)$

So we have the expression:

$6x^4y^3\cdot 21x^2y^2-9x^2y= 9x^2y\left(14x^4y^4-1\right)$

So the GCF or the greatest common factor is  

$9x^2y$