To find which expression is equal to [tex]\((3x - 4)(2x - 5)\)[/tex], we will expand the given expression step-by-step.
Step 1: Expand [tex]\((3x - 4)(2x - 5)\)[/tex] using the distributive property (also known as the FOIL method for binomials). This method requires multiplying each term in the first binomial by each term in the second binomial.
[tex]\[
(3x - 4)(2x - 5) = 3x \cdot 2x + 3x \cdot (-5) + (-4) \cdot 2x + (-4) \cdot (-5)
\][/tex]
Step 2: Perform the multiplications:
1. [tex]\(3x \cdot 2x = 6x^2\)[/tex]
2. [tex]\(3x \cdot (-5) = -15x\)[/tex]
3. [tex]\((-4) \cdot 2x = -8x\)[/tex]
4. [tex]\((-4) \cdot (-5) = 20\)[/tex]
Step 3: Add all the resultant terms together:
[tex]\[
6x^2 - 15x - 8x + 20
\][/tex]
Step 4: Combine the like terms:
[tex]\[
6x^2 - (15x + 8x) + 20 = 6x^2 - 23x + 20
\][/tex]
Therefore, the expression [tex]\((3x - 4)(2x - 5)\)[/tex] simplifies to [tex]\(6x^2 - 23x + 20\)[/tex], which matches the second option.
Thus, the correct answer is:
[tex]\[
6 x^2 - 23 x + 20
\][/tex]
