Answer:
[tex]\dfrac{a^2}{4} - 1[/tex]
Step-by-step explanation:
To simplify the expression [tex](\dfrac{a}{2} + 1)(\dfrac{a}{2} - 1)[/tex], you can use the difference of squares formula:
[tex](x + y)(x - y) = x^2 - y^2[/tex]
In this case, let [tex]x = \dfrac{a}{2} \:and \:y = 1[/tex]. Applying the difference of squares formula:
[tex](\dfrac{a}{2} + 1)(\dfrac{a}{2} - 1) = (\dfrac{a}{2})^2 - 1^2[/tex]
[tex]\dfrac{a^2}{4} - 1[/tex]
[tex]\dfrac{a^2}{4} - 1[/tex]
