Final Answer:
The product of 1/2 y² (6y²-6y+7) is 3y⁴ - 3y³ + 7y².
Step-by-step explanation:
To find the product of two polynomials, we need to first distribute the monomial, which is 1/2 y², to each term of the polynomial, 6y²-6y+7. After distributing, the product will be 3y⁴ - 3y³ + 7y². This is because 1/2 multiplied to 6y² gives us 3y⁴, multiplied to -6y gives us -3y³, and multiplied to 7 gives us 7y².
Next, we need to combine the like terms in the product. This is because like terms cannot be added or subtracted together, only multiplied. Since there are no like terms in 3y⁴ - 3y³ + 7y², the product is already in its standard form.
To recap, the product of 1/2 y² (6y²-6y+7) is 3y⁴ - 3y³ + 7y².