Alright, let's start.
Step 1: Find the GCF of the numerical coefficients
The first key factor to remember here is how to find the greatest common factor (GCF). For two numbers, the GCF is the largest number that can divide both of them without leaving a remainder. So, for the coefficients 15 and 10, the largest number that can divide both of them is 5.
So, the GCF of 15 and 10 is 5.
Step 2: Find the GCF of the variables
Now, let's move to the variables, which in this case are represented by b raised to some power. Here, we're looking at b⁽⁴⁾ and b⁽²⁾. Now, to find the GCF between two variables raised to power, we take the variable with the smaller exponent, because it's the largest power of b that divides into both b⁽⁴⁾ and b⁽²⁾.
So, the GCF of b⁽⁴⁾ and b⁽²⁾ is b⁽²⁾.
Step 3: Combine the GCFs of the coefficients and the variables
The final step is to combine the GCFs of the coefficients and the variables to get the overall solution. That's quite easy – we just stick them together.
In this case, the GCF of the coefficients is 5 and the GCF of the variables is b⁽²⁾, so we just combine those two to get '5b^2'.
So, the GCF of 15b⁽⁴⁾ and 10b⁽²⁾ is 5b⁽²⁾.
That's how we find the greatest common factor.