Question 111454
Factor the polynomial 35x^6 y^6 + 28x^3 y^4 - 7x^5 y^3, if possible.
When factoring it is sometimes easier to see if you write everything out;
Lets start by writing each term out;
{{{35x^6y^6}}}= 35(x*x*x*x*x*x)(y*y*y*y*y*y)
{{{28x^3 y^4}}}= 28(x*x*x)(y*y*y*y)
{{{7x^5 y^3}}}=7(x*x*x*x*x)(y*y*y)
Now lets cross out all commons;
Now each term has at least 3 x's and 3 y's;
{{{35x^6y^6=35(cross(x)*cross(x)*cross(x)*x*x*x)(cross(y)*cross(y)*cross(y)*y*y*y)}}}
{{{28x^3y^4= 28(cross(x)*cross(x)*cross(x))(cross(y)*cross(y)*cross(y)*y)}}}
{{{7x^5y^3=7(cross(x)*cross(x)*cross(x)*x*x)(cross(y)*cross(y)*cross(y))}}}
so we are left with;
{{{35x^3y^3}}}
{{{28y}}}
{{{7x^2}}}
we need to find the GCF between 7,28,35; which is 7;
so we are going to factor out {{{7x^3y^3}}}
{{{7x^3y^3(5x^3y^3+4y-x^2)}}}
:)