problem: Expand the product ${(2p^2 - 1)(3p^2 + 4)}$.
solution: When using the distributive property for the first time, we add the product of $2p^2 - 1$ and $3p^2$ to the product of $2p^2 - 1$ and $4$:
  
  \begin{align*}
  (2p^2 - 1)(3p^2 + 4) &= (2p^2 - 1) \cdot (3p^2) + (2p^2 - 1) \cdot 4
  \end{align*}We use the distributive property again and combine like terms:
  
  \begin{align*}
  (3p^2)(2p^2 - 1) + 4(2p^2 - 1) &= 6p^4 - 3p^2 + 8p^2 - 4\\
  &= \boxed{6p^4 + 5p^2 - 4}
  \end{align*}