Question

What is the product of 3a + 5 and 2a2 + 4a – 2?

A. 6a3 + 22a2 + 14a – 10
B. 6a3 + 22a2 + 26a –10
C. 18a3 + 10a2 + 14a – 10
D. 28a3 + 14a – 10

Answer 1

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Answer: Option A,
`\textsf{6a}^3\textsf{ + 22a}^2\textsf{ + 14a - 10}`

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Given:
`\textsf{3a + 5 and 2a}^2\textsf{ + 4a - 2}`

Find:
`\textsf{The product of the two given equations}`

Solution: The first step toward solving this problem would be to distribute the 3a and 5 to each of the values in the second equation.

• 
  `\textsf{(3a + 5)(2a}^2\textsf{ + 4a - 2)}`

• 
  `\textsf{(2a}^2\textsf{ * 3a) + (2a}^2\textsf{ * 5) + (4a * 3a) + (4a * 5) + (-2 * 3a) + (-2 * 5)}`

After doing so, we can simplify each of the expressions until we have one equation. This can be done by both some simple algebra and combining of like terms.

• 
  `\textsf{(6a}^3\textsf{) + (10a}^2\textsf{) + (12a}^2\textsf{) + (20a) + (-6a) + (-10)}`

• 
  `\textsf{6a}^3\textsf{ + 22a}^2\textsf{ + 14a + -10}`

Therefore, the correct answer to this question is Option A,
`\textsf{6a}^3\textsf{ + 22a}^2\textsf{ + 14a - 10}`.