To solve this, we need to multiply each term in the first parenthesis with every term in the second parenthesis.
![(2p +7)(3p^2 + 4p - 3)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/xv0xd91s45ijz80gkevx8v9fluphsbdid2.png)
First, we multiply each part, starting with 2p and then going to 7, pairing them with each term in the second part.
![2p(3p^2) + 2p(4p) + 2p(-3) + 7(3p^2) + 7(4p) +7(-3)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/rmzm6068nmv57akt43olnef5tuup43etpr.png)
Then, we multiply the terms together.
![6p^3 + 8p^2 - 6p + 21p^2 + 28p - 21](https://img.qammunity.org/2019/formulas/mathematics/middle-school/xd0hon6q96ie00wbbyk53wx5efak1e1mfs.png)
Lastly, we simplify the answer down by combining like terms.
![6p^3 + 29p^2 + 22p - 21](https://img.qammunity.org/2019/formulas/mathematics/middle-school/3bpy0hzdgw3d7i6kwwutxayk3bn0z4uadz.png)
The third option in this case is the correct one.