what is the product of $(3a + 2)(4a^{2}-2a + 9)$?\n$12a^{3}-2a + 18$\n$12a^{3}+6a + 9$\n$12a^{3}-6a^{2}+23a…

Explanation:

Step1: Use distributive property (FOIL - extended)

Multiply (3a) by each term in ((4a^{2}-2a + 9)) and (2) by each term in ((4a^{2}-2a + 9)). [ \begin{align*} (3a+2)(4a^{2}-2a + 9)&=3a\times(4a^{2}-2a + 9)+2\times(4a^{2}-2a + 9)\ \end{align*} ]

Step2: Calculate each product

For (3a\times(4a^{2}-2a + 9)): [ \begin{align*} 3a\times4a^{2}&=12a^{3}\ 3a\times(-2a)&=-6a^{2}\ 3a\times9&=27a \end{align*} ] For (2\times(4a^{2}-2a + 9)): [ \begin{align*} 2\times4a^{2}&=8a^{2}\ 2\times(-2a)&=-4a\ 2\times9&=18 \end{align*} ]

Step3: Combine like - terms

[ \begin{align*} &12a^{3}-6a^{2}+27a + 8a^{2}-4a+18\ =&12a^{3}+(-6a^{2}+8a^{2})+(27a-4a)+18\ =&12a^{3}+2a^{2}+23a + 18 \end{align*} ]

Answer:

(12a^{3}+2a^{2}+23a + 18) (the fourth option)