### Instruction: Expand the product ${(2p^2 - 1)(3p^2 + 4)}$.### Response: To expand a product of two binomials, I can use the distributive property and multiply each term in one binomial by each term in the other binomial.
I will write the product as ${(2p^2)(3p^2) + (2p^2)(4) + (-1)(3p^2) + (-1)(4)}$.
Now I can simplify each term by multiplying the coefficients and adding the exponents of the same base.
I get ${6p^4 + 8p^2 - 3p^2 - 4}$.
I can combine the like terms that have the same degree of p.
I get ${6p^4 + 5p^2 - 4}$.
This is the expanded form of the product.