The product of the sum and difference binomials is
[tex](x-y)(x+y)=x^2-y^2[/tex]We will use this rule to solve the question
We need to find the product of (a - 1) and (2a + 2)
At first, we will take 2 as a common factor from the second bracket
[tex]\begin{gathered} 2a+2=2(\frac{2a}{2}+\frac{2}{2}) \\ 2a+2=2(a+1) \end{gathered}[/tex]Now, we will multiply (a - 1) by 2(a + 1)
[tex](a-1)(2a-2)=2(a-1)(a+1)[/tex]By using the rule of the product of the sum and difference above, then
[tex]\begin{gathered} 2(a-1)(a+1)=2(a^2-1^2) \\ 2(a-1)(a+1)=2(a^2-1) \end{gathered}[/tex]The answer is B