Question

Find the product of (8p^2 + 7p) and (3p^3 + 2p + 7).

a) 24p^5 + 21p^2 + 14p^3 + 56p + 49
b) 24p^5 + 21p^3 + 14p^2 + 56p + 49
c) 24p^5 + 21p^2 + 14p + 7
d) 24p^5 + 21p^3 + 14p + 7

Answer 1

To find the product of (8p^2 + 7p) and (3p^3 + 2p + 7), we multiply each term in the first polynomial by each in the second, combine like terms, and obtain the final product 24p^5 + 21p^4 + 16p^3 + 70p^2 + 49p.

Step-by-step explanation:

To find the product of (8p^2 + 7p) and (3p^3 + 2p + 7), we need to apply the distributive property, also known as the FOIL method for binomials, where each term in the first polynomial is multiplied by each term in the second polynomial. Here are the steps to solve the problem:

1. Multiply 8p^2 by 3p^3: 8p^2 × 3p^3 = 24p^5.
2. Multiply 8p^2 by 2p: 8p^2 × 2p = 16p^3.
3. Multiply 8p^2 by 7: 8p^2 × 7 = 56p^2.
4. Multiply 7p by 3p^3: 7p × 3p^3 = 21p^4.
5. Multiply 7p by 2p: 7p × 2p = 14p^2.
6. Multiply 7p by 7: 7p × 7 = 49p.

Combining like terms, we get:

• 24p^5 from the first step.
• 21p^4 from the fourth step.
• 16p^3 from the second step.
• 56p^2 + 14p^2 from the third and fifth steps, which combine to 70p^2.
• 49p from the last step.

Therefore, the final product is 24p^5 + 21p^4 + 16p^3 + 70p^2 + 49p.