Final answer:
To find the value of p in the given polynomial expression, we expand and simplify the expression, compare the coefficients of like terms, and solve for p. The value of p is 11/3.
Step-by-step explanation:
To find the value of p, we need to expand and simplify the given polynomial expression.
(py²+4)(3y²-8)- 13y⁴ = 2y⁴-28y²-32
Distributing and combining like terms, we get 3py⁴ - 8py² + 12y⁴ - 32y² - 13y⁴ = 2y⁴-28y²-32
Combining like terms again, we have (3p - 13 + 2)y⁴ + (-8 - 32)y² + (-32) = 2y⁴-28y²-32
Comparing the coefficients of like terms, we get 3p - 13 + 2 = 2, -8 - 32 = -28, and -32 = -32.
Simplifying these equations gives 3p - 11 = 0, -40 = -28, and -32 = -32.
Solving for p, we have 3p - 11 = 0, which gives p = 11/3.