what is the product of (3a + 2)(4a² - 2a + 9)?\n12a³ - 2a + 18\n12a³ + 6a + 9\n12a³ - 6a² + 23a + 18\n12a³ +…
what is the product of (3a + 2)(4a² - 2a + 9)?\n12a³ - 2a + 18\n12a³ + 6a + 9\n12a³ - 6a² + 23a + 18\n12a³ + 2a² + 23a + 18
Answer
Explanation:
Step1: Use distributive property
$(3a + 2)(4a^{2}-2a + 9)=3a(4a^{2}-2a + 9)+2(4a^{2}-2a + 9)$
Step2: Distribute 3a
$3a(4a^{2}-2a + 9)=3a\times4a^{2}-3a\times2a+3a\times9 = 12a^{3}-6a^{2}+27a$
Step3: Distribute 2
$2(4a^{2}-2a + 9)=2\times4a^{2}-2\times2a+2\times9=8a^{2}-4a + 18$
Step4: Combine like - terms
$(12a^{3}-6a^{2}+27a)+(8a^{2}-4a + 18)=12a^{3}+(-6a^{2}+8a^{2})+(27a-4a)+18=12a^{3}+2a^{2}+23a + 18$
Answer:
$12a^{3}+2a^{2}+23a + 18$ (the fourth option)