To determine which of the following expressions is equal to [tex]\((3x + 2)(2x - 1)\)[/tex], let's expand and simplify the given expression step by step.
1. Expand the expression [tex]\((3x + 2)(2x - 1)\)[/tex]:
Using the distributive property, often referred to as the FOIL method for binomials, we multiply each term in the first binomial by each term in the second binomial:
[tex]\[
(3x + 2)(2x - 1) = (3x)(2x) + (3x)(-1) + (2)(2x) + (2)(-1)
\][/tex]
2. Perform the multiplications:
- [tex]\((3x)(2x) = 6x^2\)[/tex]
- [tex]\((3x)(-1) = -3x\)[/tex]
- [tex]\((2)(2x) = 4x\)[/tex]
- [tex]\((2)(-1) = -2\)[/tex]
3. Combine all the terms:
[tex]\[
6x^2 + (-3x) + 4x + (-2)
\][/tex]
4. Simplify by combining like terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-3x + 4x = x\)[/tex]
Therefore, the expression simplifies to:
[tex]\[
6x^2 + x - 2
\][/tex]
So, the expanded form of [tex]\((3x + 2)(2x - 1)\)[/tex] is [tex]\(6x^2 + x - 2\)[/tex].
Hence, the expression that is equal to [tex]\((3x + 2)(2x - 1)\)[/tex] is [tex]\(6x^2 + x - 2\)[/tex].
