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Which of the following expressions is equal to [tex][tex]$(3x + 2)(2x - 1)$[/tex][/tex]?

A. [tex]6x^2 + x - 2[/tex]
B. [tex]6x^2 - x - 2[/tex]
C. [tex]6x^2 + x + 2[/tex]
D. [tex]6x^2 - x + 2[/tex]

Sagot :

GinnyAnsweridn
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].
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