Final answer:
To factor the expression 14x²y² + 42xy³ using the greatest common factor (GCF), the GCF is found by identifying the highest power of each variable that appears in both terms. Factoring out the GCF, we get 14xy²(x + 3y).
Step-by-step explanation:
To factor the expression 14x²y² + 42xy³ using the greatest common factor (GCF), we need to find the common factors between the terms. The GCF is found by identifying the highest power of each variable that appears in both terms. In this case, the GCF is 14xy².
14x²y² + 42xy³ = 14xy²(x + 3y)
Factoring out the GCF, we get: 14xy²(x + 3y).