Question

what is the product of (3a + 2)(4a² - 2a + 9)?
12a³ - 2a + 18
12a³ + 6a + 9
12a³ - 6a² + 23a + 18
12a³ + 2a² + 23a + 18

Explanation:

Step1: Distribute \(3a\)

Multiply \(3a\) with each term in \(4a^2 - 2a + 9\):
\(3a \times 4a^2 = 12a^3\), \(3a \times (-2a) = -6a^2\), \(3a \times 9 = 27a\).

Step2: Distribute \(2\)

Multiply \(2\) with each term in \(4a^2 - 2a + 9\):
\(2 \times 4a^2 = 8a^2\), \(2 \times (-2a) = -4a\), \(2 \times 9 = 18\).

Step3: Combine like terms

Add the results from Step1 and Step2:
\(12a^3 - 6a^2 + 27a + 8a^2 - 4a + 18\).
Combine \(a^2\) terms: \(-6a^2 + 8a^2 = 2a^2\).
Combine \(a\) terms: \(27a - 4a = 23a\).
Final expression: \(12a^3 + 2a^2 + 23a + 18\).

Answer:

\(12a^3 + 2a^2 + 23a + 18\) (the fourth option: \(12a^3 + 2a^2 + 23a + 18\))