Question

How do you factor out the GCF of `40a ^ { 6} b ^ { 5} - 50a^ { 5} b ^ { 6}`?

Answer 1

Find the largest coefficient and degree that can divide all values.

Explanation:

The GCF is the greatest factor that can divide all terms (unless you choose not to factor it out).

First off, we have to find a value that can divide the coefficients.

In this case, it is `10`. No other number can divide `40` and `50`.

Therefore, the first number is `10`.

`40a^6b^5 - 50a^5b^6`

`10(4a^6b^5 - 5a^5b^6)`

The next step are the variables. For these, we must use the largest degree that all terms share. For `a`, it is `5` and same for `b`.

`10a^5b^5(4b - 5a)`

And that's it.

Hope this helps :)