Sure, let's find the product of the given expressions and then simplify it.
Given expressions:
[tex]\[ (2b - 2)(4b - 3) \][/tex]
Step 1: Expand the expression using the distributive property (FOIL method).
This means that each term in the first bracket should be multiplied by each term in the second bracket.
[tex]\[ (2b - 2)(4b - 3) \][/tex]
[tex]\[ = (2b \cdot 4b) + (2b \cdot -3) + (-2 \cdot 4b) + (-2 \cdot -3) \][/tex]
Now, compute each multiplication separately:
1. \( 2b \cdot 4b = 8b^2 \)
2. \( 2b \cdot -3 = -6b \)
3. \( -2 \cdot 4b = -8b \)
4. \( -2 \cdot -3 = 6 \)
Step 2: Combine like terms.
[tex]\[ 8b^2 - 6b - 8b + 6 \][/tex]
[tex]\[ = 8b^2 - 14b + 6 \][/tex]
Therefore, the expanded and simplified form of the product is:
[tex]\[ 8b^2 - 14b + 6 \][/tex]
A further simplification can also be:
[tex]\[ 2(b - 1)(4b - 3) \][/tex]
Thus, the final simplified answer to the multiplication of the expressions \((2b - 2)\) and \((4b - 3)\) is:
[tex]\[ \boxed{2(b-1)(4b-3)} \][/tex]
