How do you factor out the greatest common factor of 112x^9y^9 + 144x^5y^5+128x^7y^3?

2 Answers
Mar 22, 2017

16x^5y^3

Explanation:

First, you look at only the coefficients. Find all of their prime factors, in this case they are respectively: 7*2*2*2*2, 3*3*2*2*2*2, and 2*2*2*2*2*2*2. Once you've done that, determine every factor that they have in common. In this case, they all have at least four two's. Once those four two's are taken out though, they have nothing else all in common so 2^4 will be our coefficient which is 16.

Now, look at the two variables. Whichever term has the lowest power of x is the power of x that you will use because the other terms have at LEAST that power of x so they have that in common. In this case it is 5. For y it is 3. So the answer is 16x^5y^3. Hope I helped!

Mar 22, 2017

16x^5y^3(7x^4y^6+9y^2+8x^2)

Explanation:

112x^9y^9+144x^5y^5+128x^7y^3

:.=16x^5y^3(7x^4y^6+9y^2+8x^2)