Final answer:
The greatest common factor of 18xy², 18xy², and 42y³ is 6xy², which is derived by finding the highest power of each factor common to all terms.
Step-by-step explanation:
The goal is to find the greatest common factor (GCF) of the three given expressions: 18xy², 18xy², and 42y³. To find the GCF, we need to look for the highest exponent common to all terms in each factor.
- For the numerical coefficients (18 and 42), the GCF is 6 since 6 is the largest number that divides both 18 and 42 without leaving a remainder.
- For the variable 'x', the GCF is 'x' because it's the only power of 'x' that is present in all terms.
- For 'y', the GCF is y² since y² is the highest power of 'y' that divides evenly into both y² and y³.
Therefore, the GCF of 18xy², 18xy², and 42y³ is 6xy².