Final answer:
The greatest common divisor (GCD) of 6b and 2b² is 2b. We arrived at this answer by factoring the terms and extracting their common factors.
Step-by-step explanation:
The student is asking to find the greatest common divisor (GCD) of the two algebraic terms 6b and 2b². To find the GCD of these terms, we need to factor out the common factors in each term.
The first term, 6b, can be factored into 2 * 3 * b. The second term, 2b², is 2 * b * b. The common factors are a '2' and a single 'b' from both terms.
Therefore, the GCD of 6b and 2b² is 2b. This means that 2b is the largest expression that divides both 6b and 2b² without any remainder.