(3x+4)(x-2)
A) 3x²-2x-8
B) x-8
C) 3x-2x-8
D) 3x²+2x+8
Solution:
Using the FOIL method, we get:
(3x+4)(x-2) = (3x)(x) + (3x)(-2) + (4)(x) + (4)(-2)
= 3x² - 6x + 4x - 8
= 3x² - 2x - 8
Therefore, the answer is A) 3x²-2x-8.
To multiply the given expression, (3x+4)(x-2), you can use the distributive property. Here are the steps:
1. Multiply the first terms of each binomial: (3x)(x) = 3x².
2. Multiply the outer terms of each binomial: (3x)(-2) = -6x.
3. Multiply the inner terms of each binomial: (4)(x) = 4x.
4. Multiply the last terms of each binomial: (4)(-2) = -8.
Now, let's add up all the results:
3x² - 6x + 4x - 8.
Combine like terms:
3x² - 2x - 8.
So, the correct answer is A) 3x² - 2x - 8.