Final answer:
To find the product of 4x^3y and -2x^2y, you multiply the coefficients and combine the like terms. The product is -8x^5y^2.
Step-by-step explanation:
To find the product of 4x^3y and -2x^2y, you multiply the coefficients and combine the like terms. The coefficient of 4x^3y is 4 and the coefficient of -2x^2y is -2. Multiplying these coefficients gives -8. To multiply the variables x, you add the exponents, resulting in x^(3+2) = x^5. Similarly, for y, you add the exponents, resulting in y^(1+1) = y^2. Therefore, the product is -8x^5y^2.