Final answer:
To factor out the greatest common monomial of the expression 4x²y² + 8x³y², the GCF is determined to be 4x²y², resulting in the factorized form 4x²y²(1 + 2x).
Step-by-step explanation:
The student's question is about finding the greatest common monomial factor from a given algebraic expression. To factor out this greatest common factor (GCF), we look for the highest power of each variable that is common to all terms in the expression as well as the largest coefficient that divides all the coefficients.
The expression is 4x²y² + 8x³y². Both terms have a x²y² and the coefficients are both divisible by 4, so the GCF is 4x²y². We divide each term in the expression by this GCF:
Factorization: 4x²y²(1 + 2x)