what is the product of $(2p + 7)(3p^{2}+4p - 3)$?\n$6p^{3}+29p^{2}-34p + 21$\n$6p^{3}+29p^{2}-22p +…

what is the product of $(2p + 7)(3p^{2}+4p - 3)$?\n$6p^{3}+29p^{2}-34p + 21$\n$6p^{3}+29p^{2}-22p + 21$\n$6p^{3}+29p^{2}+22p - 21$\n$6p^{3}+29p^{2}+34p - 21$

what is the product of $(2p + 7)(3p^{2}+4p - 3)$?\n$6p^{3}+29p^{2}-34p + 21$\n$6p^{3}+29p^{2}-22p + 21$\n$6p^{3}+29p^{2}+22p - 21$\n$6p^{3}+29p^{2}+34p - 21$

Answer

Explanation:

Step1: Use the distributive property (FOIL method)

$$(2p + 7)(3p^{2}+4p - 3)=2p\times(3p^{2}+4p - 3)+7\times(3p^{2}+4p - 3)$$

Step2: Multiply each term

  • For (2p\times(3p^{2}+4p - 3)):
    • (2p\times3p^{2}=6p^{3})
    • (2p\times4p = 8p^{2})
    • (2p\times(-3)=-6p)
  • For (7\times(3p^{2}+4p - 3)):
    • (7\times3p^{2}=21p^{2})
    • (7\times4p = 28p)
    • (7\times(-3)=-21)

Step3: Combine like - terms

[ \begin{align*} &6p^{3}+8p^{2}-6p + 21p^{2}+28p-21\ =&6p^{3}+(8p^{2}+21p^{2})+( - 6p+28p)-21\ =&6p^{3}+29p^{2}+22p-21 \end{align*} ]

Answer:

(6p^{3}+29p^{2}+22p - 21) (the third option)