To find the expression that is equal to [tex]\((6x - 4)(3x - 1)\)[/tex], let's expand and simplify it step by step.
1. Standard form:
We need to use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first binomial by each term in the second binomial.
2. Multiplying the terms:
[tex]\[
(6x - 4)(3x - 1) = (6x \cdot 3x) + (6x \cdot -1) + (-4 \cdot 3x) + (-4 \cdot -1)
\][/tex]
3. Calculating each multiplication:
- [tex]\(6x \cdot 3x = 18x^2\)[/tex]
- [tex]\(6x \cdot -1 = -6x\)[/tex]
- [tex]\(-4 \cdot 3x = -12x\)[/tex]
- [tex]\(-4 \cdot -1 = 4\)[/tex]
4. Adding all these products together:
[tex]\[
18x^2 - 6x - 12x + 4
\][/tex]
5. Combine like terms:
- The terms [tex]\(-6x\)[/tex] and [tex]\(-12x\)[/tex] are like terms. Combine them:
[tex]\[
-6x - 12x = -18x
\][/tex]
6. Write the final expanded and simplified expression:
[tex]\[
18x^2 - 18x + 4
\][/tex]
Thus, after expanding and simplifying [tex]\((6x - 4)(3x - 1)\)[/tex], the resulting expression is:
[tex]\[
\boxed{18x^2 - 18x + 4}
\][/tex]
So the correct answer from the given options is:
[tex]\[ 18x^2 - 18x + 4 \][/tex]
