Final answer:
To simplify the given expression using the distributive property and the product rule of exponents, we can expand the expression using the distributive property and then simplify it by applying the product rule of exponents. The simplified expression will be -4xy^2 + 2xy + 8y.
Step-by-step explanation:
The given expression is (y)(-4xy + 2x + 8). To simplify this expression, we can apply the distributive property of multiplication over addition/subtraction. According to the distributive property, when we multiply a number or variable with a sum or difference, we distribute the multiplication to each term within the parentheses. So, applying the distributive property, we get:
(y)(-4xy) + (y)(2x) + (y)(8)
-4xy^2 + 2xy + 8y
Now, let's simplify the expression using the product rule of exponents. According to the product rule of exponents, when we multiply variables with the same base, we add their exponents. In this case, the base is 'y'. Therefore, the term '-4xy^2' can be written as '-4x * y^2'. Similarly, the term '2xy' remains the same. Simplifying further, we get:
-4xy^2 + 2xy + 8y
Learn more about simplifying expressions using the distributive property and the product rule of exponents