To find the fully expanded form of the expression [tex]\((4x - 1)(-3x + 2)\)[/tex], we can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Let's go through the steps in detail:
1. Expand the product [tex]\((4x - 1)(-3x + 2)\)[/tex]:
[tex]\[
(4x - 1)(-3x + 2)
\][/tex]
Distribute each term in the first binomial with each term in the second binomial.
2. First, multiply [tex]\(4x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
4x \cdot (-3x) = -12x^2
\][/tex]
3. Next, multiply [tex]\(4x\)[/tex] by [tex]\(2\)[/tex]:
[tex]\[
4x \cdot 2 = 8x
\][/tex]
4. Then, multiply [tex]\(-1\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
-1 \cdot (-3x) = 3x
\][/tex]
5. Finally, multiply [tex]\(-1\)[/tex] by [tex]\(2\)[/tex]:
[tex]\[
-1 \cdot 2 = -2
\][/tex]
6. Combine all these results:
[tex]\[
-12x^2 + 8x + 3x - 2
\][/tex]
7. Simplify by combining like terms [tex]\(8x\)[/tex] and [tex]\(3x\)[/tex]:
[tex]\[
-12x^2 + 11x - 2
\][/tex]
Therefore, the fully expanded form of [tex]\((4x - 1)(-3x + 2)\)[/tex] is:
[tex]\[
-12x^2 + 11x - 2
\][/tex]
The correct choice from the given options is:
[tex]\[
-12x^2 + 11x - 2
\][/tex]
